{"id":53777,"date":"2019-12-10T00:00:00","date_gmt":"2019-12-09T21:00:00","guid":{"rendered":"https:\/\/prohoster.info\/blog\/blog_prohoster\/privodim-uravnenie-linejnoj-regressii-v-matrichnyj-vid"},"modified":"2020-02-18T14:01:42","modified_gmt":"2020-02-18T11:01:42","slug":"privodim-uravnenie-linejnoj-regressii-v-matrichnyj-vid","status":"publish","type":"post","link":"https:\/\/prohoster.info\/cs\/blog\/news\/privodim-uravnenie-linejnoj-regressii-v-matrichnyj-vid","title":{"rendered":"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/47507c0ae01db89c623d94f540c22aea.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\nC\u00edlem \u010dl\u00e1nku je poskytnout podporu za\u010d\u00ednaj\u00edc\u00edm datov\u00fdm v\u011bdc\u016fm. V <noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/474602\/\">p\u0159edchoz\u00ed \u010dl\u00e1nku<\/a><\/noindex> t\u011bchto p\u0159\u00edkladech jsme si uk\u00e1zali t\u0159i zp\u016fsoby \u0159e\u0161en\u00ed rovnice line\u00e1rn\u00ed regrese: analytick\u00e9 \u0159e\u0161en\u00ed, gradientn\u00ed sestup a stochastick\u00fd gradientn\u00ed sestup. Pro analytick\u00e9 \u0159e\u0161en\u00ed jsme pou\u017eili vzorec <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/50b913c04204ae6400ca1676cca57d18.jpg\" style=\"display:block;margin: 0 auto;\" \/>. V tomto \u010dl\u00e1nku, jak napov\u00edd\u00e1 n\u00e1zev, zd\u016fvodn\u00edme pou\u017eit\u00ed tohoto vzorce, jin\u00fdmi slovy, odvod\u00edme si ho sami. <\/p>\n<p>Pro\u010d m\u00e1 smysl v\u011bnovat zv\u00fd\u0161enou pozornost vzorci <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/9d44749d6f8b509b3167a25f0c583f7f.jpg\" style=\"display:block;margin: 0 auto;\" \/>? <\/p>\n<p>Pr\u00e1v\u011b z maticov\u00e9 rovnice v\u011bt\u0161inou za\u010d\u00edn\u00e1 sezn\u00e1men\u00ed s line\u00e1rn\u00ed regres\u00ed. P\u0159itom se podrobn\u00e9 v\u00fdpo\u010dty toho, jak byl vzorec odvozen, objevuj\u00ed z\u0159\u00eddka.<br \/>\n<noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><br \/>\nNap\u0159\u00edklad na kurzech strojov\u00e9ho u\u010den\u00ed od Yandexu, kdy\u017e se poslucha\u010di seznamuj\u00ed s regularizac\u00ed, se doporu\u010duje vyu\u017e\u00edt funkce z knihovny <i>sklearn<\/i>, p\u0159i\u010dem\u017e se nezmi\u0148uje ani slovo o maticov\u00e9m zobrazen\u00ed algoritmu. V tuto chv\u00edli m\u016f\u017ee \u010d\u00e1st poslucha\u010d\u016f dostat chu\u0165 se v t\u00e9to problematice pod\u00edvat podrobn\u011bji \u2014 napsat k\u00f3d bez pou\u017eit\u00ed p\u0159edem p\u0159ipraven\u00fdch funkc\u00ed. A k tomu je pot\u0159eba nejprve p\u0159edstavit rovnici s regulariz\u00e1torem v maticov\u00e9 podob\u011b. Tento \u010dl\u00e1nek pr\u00e1v\u011b umo\u017en\u00ed t\u011bm, kte\u0159\u00ed cht\u011bj\u00ed z\u00edskat takov\u00e9 dovednosti. Poj\u010fme na to.<\/p>\n<h2>Po\u010d\u00e1te\u010dn\u00ed podm\u00ednky<\/h2>\n<p><\/p>\n<h3>C\u00edlov\u00e9 ukazatele<\/h3>\n<p>\nM\u00e1me \u0159adu hodnot c\u00edlov\u00e9ho ukazatele. Nap\u0159\u00edklad c\u00edlov\u00fdm ukazatelem m\u016f\u017ee b\u00fdt cena n\u011bjak\u00e9ho aktiva: ropa, zlato, p\u0161enice, dolar atd. P\u0159i\u010dem\u017e pod \u0159adou hodnot c\u00edlov\u00e9ho ukazatele rozum\u00edme po\u010det pozorov\u00e1n\u00ed. Takov\u00fdmi pozorov\u00e1n\u00edmi mohou b\u00fdt nap\u0159\u00edklad m\u011bs\u00ed\u010dn\u00ed ceny ropy za rok, tedy budeme m\u00edt 12 hodnot c\u00edlov\u00e9ho ukazatele. Za\u010dn\u011bme zav\u00e1d\u011bt ozna\u010den\u00ed. Ozna\u010dme ka\u017edou hodnotu c\u00edlov\u00e9ho ukazatele jako <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d974b10a558b8a917aca3dd7d16e9a7d.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Celkem m\u00e1me <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/5e826824b32c20c20eb15b276c544583.jpg\" style=\"display:block;margin: 0 auto;\" \/> pozorov\u00e1n\u00ed, tak\u017ee na\u0161e pozorov\u00e1n\u00ed lze p\u0159edstavit jako <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/599bcd56d392e21dcf63b72b07edcbc5.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<h3>Regresory<\/h3>\n<p>\nBudeme pova\u017eovat, \u017ee existuj\u00ed faktory, kter\u00e9 do ur\u010dit\u00e9 m\u00edry vysv\u011btluj\u00ed hodnoty c\u00edlov\u00e9ho ukazatele. Nap\u0159\u00edklad na kurz p\u00e1ru dolar\/rubl m\u00e1 siln\u00fd vliv cena ropy, sazba FRS a dal\u0161\u00ed. Takov\u00e9 faktory se naz\u00fdvaj\u00ed regresory. Ka\u017ed\u00e9 hodnot\u011b c\u00edlov\u00e9ho ukazatele by m\u011blo odpov\u00eddat hodnota regresoru, co\u017e znamen\u00e1, \u017ee pokud m\u00e1me 12 c\u00edlov\u00fdch ukazatel\u016f za ka\u017ed\u00fd m\u011bs\u00edc v roce 2018, pak tak\u00e9 mus\u00edme m\u00edt 12 hodnot regresor\u016f za stejn\u00e9 obdob\u00ed. Ozna\u010d\u00edme hodnoty ka\u017ed\u00e9ho regresoru jako <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d49b372bea0c1d50c21681357f85610a.jpg\" style=\"display:block;margin: 0 auto;\" \/>. P\u0159edpokl\u00e1dejme, \u017ee v na\u0161em p\u0159\u00edpad\u011b m\u00e1me <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/61a94efcc11446ebee920870a684c216.jpg\" style=\"display:block;margin: 0 auto;\" \/> regresor\u016f (tj. <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2699691a567d694e61e6fdb288bc9b54.jpg\" style=\"display:block;margin: 0 auto;\" \/> faktor\u016f, kter\u00e9 maj\u00ed vliv na hodnoty c\u00edlov\u00e9ho ukazatele). Na\u0161e regresory tedy m\u016f\u017eeme p\u0159edstavit n\u00e1sleduj\u00edc\u00edm zp\u016fsobem: pro 1. regresor (nap\u0159\u00edklad cena ropy): <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/79434bf84a9b18f83602225f43e68cc7.jpg\" style=\"display:block;margin: 0 auto;\" \/>, pro 2. regresor (nap\u0159\u00edklad sazba FRS): <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/378180ee8fdaa8f6aca7bc8300a21207.jpg\" style=\"display:block;margin: 0 auto;\" \/>, pro &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/fc70caea64d3bc2aa5e797257f6627fb.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00ed&#187; regresor: <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/90499d34f1577681de33966a024faf2e.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<h3>Z\u00e1vislost c\u00edlov\u00fdch ukazatel\u016f na regresorech<\/h3>\n<p>\nP\u0159edpokl\u00e1dejme, \u017ee z\u00e1vislost c\u00edlov\u00e9ho ukazatele <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/aa7d30d8fb9ca837144d34423aed5a77.jpg\" style=\"display:block;margin: 0 auto;\" \/> od regressor\u016f &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/97a9aba33249a8b9eb3a61bdfc794287.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00edho&#187; pozorov\u00e1n\u00ed m\u016f\u017ee b\u00fdt vyj\u00e1d\u0159eno pomoc\u00ed rovnice line\u00e1rn\u00ed regrese ve tvaru:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/ff892eb01b0bb830a94cacf62168d142.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>, kde <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/27d8f05c058f7b42aac3a4d3fab1db51.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/cd438a2e58f8db5e9f1df8b387b18cff.jpg\" style=\"display:block;margin: 0 auto;\" \/>-\u00e9&#187; hodnota regresoru od 1 do <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/21513049bf0d7b13af73d53605089765.jpg\" style=\"display:block;margin: 0 auto;\" \/>,<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/268ca408ca89b7846220c920e2078d5d.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 po\u010det regresor\u016f od 1 do <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/8be331a5b16bf3796e6200e77ee58c09.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/49558388879a529fc342848d80b60d32.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 \u00fahlov\u00e9 koeficienty, kter\u00e9 p\u0159edstavuj\u00ed velikost, o kterou se pr\u016fm\u011brn\u011b zm\u011bn\u00ed vypo\u010d\u00edt\u00e1van\u00fd c\u00edlov\u00fd ukazatel p\u0159i zm\u011bn\u011b regresoru. <\/p>\n<p>Jin\u00fdmi slovy, pro ka\u017ed\u00fd (s v\u00fdjimkou <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/fcc00174a0090f9974712c779718f13c.jpg\" style=\"display:block;margin: 0 auto;\" \/>) regresor ur\u010d\u00edme \"sv\u016fj\" koeficient <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/c40688d883e7a22b52905be2517a91f9.jpg\" style=\"display:block;margin: 0 auto;\" \/>, pot\u00e9 n\u00e1sob\u00edme koeficienty hodnotami regressor\u016f &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/48db80e36602c8a55eba1e518b1e3efa.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00edho&#187; pozorov\u00e1n\u00ed, v d\u016fsledku toho dostaneme ur\u010dit\u00e9 p\u0159ibl\u00ed\u017een\u00ed &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/a182d4ce402fa8b1d8f631ffddd5e63e.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00edho&#187; c\u00edlov\u00e9ho ukazatele.<\/p>\n<p>Proto pot\u0159ebujeme nal\u00e9zt takov\u00e9 koeficienty <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/81edeafa5c9539a4b168d5b40027ffd0.jpg\" style=\"display:block;margin: 0 auto;\" \/>, p\u0159i kter\u00fdch budou hodnoty na\u0161\u00ed aproxima\u010dn\u00ed funkce <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/84ae78e0b61fd87769ae120f903f2a8a.jpg\" style=\"display:block;margin: 0 auto;\" \/> um\u00edst\u011bny co nejbl\u00ed\u017ee hodnot\u00e1m c\u00edlov\u00fdch ukazatel\u016f.<\/p>\n<h3>Hodnocen\u00ed kvality aproxima\u010dn\u00ed funkce<\/h3>\n<p>\nUr\u010d\u00edme hodnocen\u00ed kvality aproxima\u010dn\u00ed funkce metodou nejmen\u0161\u00edch \u010dtverc\u016f. Funkce hodnocen\u00ed kvality v tomto p\u0159\u00edpad\u011b nabude n\u00e1sleduj\u00edc\u00edho tvaru:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d50c5c70fda27cf18308baa31c2366a5.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Pot\u0159ebujeme nal\u00e9zt takov\u00e9 hodnoty koeficient\u016f $w$, p\u0159i kter\u00fdch bude hodnota <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e2ad7197c6ca2c9ac986a62fcfef1f7d.jpg\" style=\"display:block;margin: 0 auto;\" \/> co nejmen\u0161\u00ed.<\/p>\n<h2>P\u0159evedeme rovnici do maticov\u00e9ho tvaru<\/h2>\n<p><\/p>\n<h3>Vektorov\u00e9 zobrazen\u00ed<\/h3>\n<p>\nNejd\u0159\u00edve, abychom si usnadnili pr\u00e1ci, je t\u0159eba se zam\u011b\u0159it na rovnici line\u00e1rn\u00ed regrese a v\u0161imnout si, \u017ee prvn\u00ed koeficient <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/4b34e4c0e260b7bc143e95e83169fcc9.jpg\" style=\"display:block;margin: 0 auto;\" \/> nen\u00ed n\u00e1sobena \u017e\u00e1dn\u00fdm regresorem. P\u0159itom, kdy\u017e data p\u0159evedeme do maticov\u00e9 podoby, v\u00fd\u0161e uveden\u00e1 okolnost zna\u010dn\u011b zkomplikuje v\u00fdpo\u010dty. V t\u00e9to souvislosti navrhujeme zav\u00e9st je\u0161t\u011b jeden regresor pro prvn\u00ed koeficient <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/6b6c662ff0c499870d0f119589ae2b44.jpg\" style=\"display:block;margin: 0 auto;\" \/> a p\u0159irovn\u00e1me ho k jedn\u00e9. P\u0159esn\u011bji, ka\u017edou &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/7c0aa6c3c797066208fb19a638ef513f.jpg\" style=\"display:block;margin: 0 auto;\" \/>-ou&#187; hodnotu tohoto regresoru p\u0159irovn\u00e1me k jedn\u00e9 - v\u017edy\u0165 p\u0159i n\u00e1soben\u00ed jedni\u010dkou se z hlediska v\u00fdsledk\u016f v\u00fdpo\u010dt\u016f nic nezm\u011bn\u00ed, a z pohledu pravidel n\u00e1soben\u00ed matic v\u00fdznamn\u011b zkr\u00e1t\u00edme na\u0161e utrpen\u00ed. <\/p>\n<p>Nyn\u00ed, na n\u011bjakou dobu, s c\u00edlem zjednodu\u0161en\u00ed materi\u00e1lu, p\u0159edpokl\u00e1dejme, \u017ee m\u00e1me pouze jeden &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/eac0db64e38d3ce6b5a0303393704fab.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00ed&#187; pozorov\u00e1n\u00ed. Pot\u00e9, p\u0159edstavme si hodnoty regressor\u016f &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/ca79caf5f669c549b97d51ce1cb6f7cd.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00edho&#187; pozorov\u00e1n\u00ed jako vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/63e0cf2d3b09577dfd6d76718864e56a.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/bff53727ebff61bbbe97ca02a132338d.jpg\" style=\"display:block;margin: 0 auto;\" \/> m\u00e1 rozm\u011brnost <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/f87f7646f1f53f041e53c8f63bb30405.jpg\" style=\"display:block;margin: 0 auto;\" \/>, to znamen\u00e1 <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/bda60053e47e7a5324106d5e6cdedbab.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u0159\u00e1dk\u016f a 1 sloupec:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/fc1a58c18e118375c3bee17e1a3143d9.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Hledan\u00e9 koeficienty si p\u0159edstavme ve form\u011b vektoru <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/4c6805c97148d50d3233e183a4690b47.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kter\u00fd m\u00e1 rozm\u011brnost <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/8cbddba5ac5f8c0e8f5d80c5dd5a4c6f.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/ebcf96a3aa612fbdf10864c010787d0e.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Rovnice line\u00e1rn\u00ed regrese pro &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/6a93855293a06ea44f48077c315dde79.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00ed&#187; pozorov\u00e1n\u00ed nabude tvaru: <\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e73499da0077212806ea3ce5d639bb9c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Funkce hodnocen\u00ed kvality line\u00e1rn\u00edho modelu nabude tvaru:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/a33c79a345dccc9e1fce3a32d53b2164.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>V\u0161imn\u011bte si, \u017ee v souladu s pravidly maticov\u00e9ho n\u00e1soben\u00ed, bylo nutn\u00e9 transponovat vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3e551ab86fc872959afe9ea10344549e.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<h3>Maticov\u00e1 reprezentace<\/h3>\n<p>\nV d\u016fsledku n\u00e1soben\u00ed vektor\u016f z\u00edsk\u00e1me \u010d\u00edslo: <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/1889e5ba7053a652c7ad1ea6b37627ab.jpg\" style=\"display:block;margin: 0 auto;\" \/>, co\u017e bylo o\u010dek\u00e1v\u00e1no. Toto \u010d\u00edslo je p\u0159ibl\u00ed\u017een\u00ed &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/255557422b97a46c2575f2279c656bd0.jpg\" style=\"display:block;margin: 0 auto;\" \/>-n\u00edho&#187; c\u00edlov\u00e9ho ukazatele. Ale my pot\u0159ebujeme p\u0159ibl\u00ed\u017een\u00ed ne jednoho hodnoty c\u00edlov\u00e9ho ukazatele, ale v\u0161ech. Za t\u00edmto \u00fa\u010delem zap\u00ed\u0161eme v\u0161echny &#171;<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/63289920f39f55a57a48b48255ad96dd.jpg\" style=\"display:block;margin: 0 auto;\" \/>-\u00e9&#187; regresory ve form\u00e1tu matice <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3a003dcab41a7c3c5cff534fd0b91e3b.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Z\u00edskan\u00e1 matice m\u00e1 rozm\u011brnost <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3435a6daffd0abb5961629671c8fa441.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3901fc083e9dcf646d9d3da4c06de85d.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Nyn\u00ed rovnice line\u00e1rn\u00ed regrese nabude tvaru:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/73e7317b0815f3d8bdf514907d0c0a90.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Ozna\u010dme hodnoty c\u00edlov\u00fdch ukazatel\u016f (v\u0161echny <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e3b9482a385dd9be37c568c4e738883e.jpg\" style=\"display:block;margin: 0 auto;\" \/>) za vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/55cdadb0e1c9c9a1f39d918160f51c07.jpg\" style=\"display:block;margin: 0 auto;\" \/> o rozm\u011brnosti <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/62d6246fd9a76e9da4bea15d44456d68.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/8b7626b09765e9e059c88d21b4593c31.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Nyn\u00ed m\u016f\u017eeme napsat v maticov\u00e9m form\u00e1tu rovnici hodnocen\u00ed kvality line\u00e1rn\u00edho modelu:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/394b3b15cc03bb921d7ca55c2ec3db6c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Vlastn\u011b, z tohoto vzorce d\u00e1le z\u00edsk\u00e1v\u00e1me n\u00e1m zn\u00e1m\u00fd vzorec <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/70f26b6f641c29eb4de0211778b0b207.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Jak to d\u011bl\u00e1me? Rozv\u00edjej\u00ed se z\u00e1vorky, prov\u00e1d\u00ed se diferenciace, transformuj\u00ed se z\u00edskan\u00e9 v\u00fdrazy atd., a t\u00edm se nyn\u00ed budeme zab\u00fdvat.<\/p>\n<h2>Maticov\u00e9 transformace<\/h2>\n<p><\/p>\n<h3>Rozvineme z\u00e1vorky<\/h3>\n<p>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e7d2ff15007e174e94cf65793538f6df.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2ef9bcd45ff0b3268aa40445d38b3ec0.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<h3>P\u0159iprav\u00edme rovnici pro diferenciaci<\/h3>\n<p>\nK tomu provedeme n\u011bkter\u00e9 transformace. V n\u00e1sleduj\u00edc\u00edch v\u00fdpo\u010dtech bude pohodln\u011bj\u0161\u00ed, pokud bude vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e14c5e74d164b3fc53f654d1f5b0be41.jpg\" style=\"display:block;margin: 0 auto;\" \/> p\u0159edstavov\u00e1n na za\u010d\u00e1tku ka\u017ed\u00e9ho sou\u010dinu v rovnici.<\/p>\n<h4>Transformace 1<\/h4>\n<p>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/f2a2bf00b2ebbd266789420b0aa33404.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Jak se to stalo? Abychom na tuto ot\u00e1zku odpov\u011bd\u011bli, sta\u010d\u00ed se pod\u00edvat na rozm\u011bry n\u00e1soben\u00fdch matic a vid\u011bt, \u017ee na v\u00fdstupu dost\u00e1v\u00e1me \u010d\u00edslo, nebo jinak, <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e6e75542a7ab114c0dc7277593ccc86d.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p>Zap\u00ed\u0161eme rozm\u011bry maticov\u00fdch v\u00fdraz\u016f.<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/9913d89c711c919ea5dcc5f6c2beaadf.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/b8b65ace6ac8a6b5218b9d79f6eceff1.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/b1982bd25dc54b29220c1021c05880ef.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<h4>Transformace 2<\/h4>\n<p>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3801b847f4e69894dc0e19ceefb5de55.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Zapi\u0161me obdobn\u011b jako u transformace 1<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/4bb7dbb1211c7e15ba18a8b2a0f63191.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/60e7b41a69d3fb229e36f84960527769.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Na v\u00fdstupu dost\u00e1v\u00e1me rovnici, kterou budeme muset diferencovat:<br \/>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2c3b23bef5eba43159baf5be3effe604.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<h2>Diferencujeme funkci hodnocen\u00ed kvality modelu<\/h2>\n<p>\nDiferencujeme podle vektoru <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/7f408dd080459692d93f343528219bd6.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/fb6025293b318051b926913bc8e5849c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d5d089a76ceeda9dae631e9af478df36.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/4dca6e16f82114a777ec2d5dbd6df998.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/efb26c3a7e8b40de68d8aba115f09feb.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Ot\u00e1zek pro\u010d <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e814552115f81a72fa60a988b7644af6.jpg\" style=\"display:block;margin: 0 auto;\" \/> by nem\u011blo b\u00fdt, ale operace p\u0159i ur\u010dov\u00e1n\u00ed derivac\u00ed ve dvou dal\u0161\u00edch v\u00fdrazech podrobn\u011bji prozkoum\u00e1me.<\/p>\n<h3>Diferencov\u00e1n\u00ed 1<\/h3>\n<p>\nOtev\u0159eme diferencov\u00e1n\u00ed: <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/6e00a4d10e726babe1d058c9d2ce7723.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Abychom ur\u010dili derivaci matice nebo vektoru, mus\u00edme se pod\u00edvat, co je uvnit\u0159. D\u00edv\u00e1me se:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/edccede10d4d013897fefdf65e81add5.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2263c941aa42adc1ef20031fc2facf17.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/cd4c1ec8f6f5934f24fa7c21ebe51358.jpg\" style=\"display:block;margin: 0 auto;\" \/> <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d75a93eaae356ef96390b4e95e2d5cb9.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Ozna\u010dme sou\u010din matic <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/75083779f507ad45545f6e10abb3902d.jpg\" style=\"display:block;margin: 0 auto;\" \/> p\u0159es matici <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/10290d0fb2886757f5060bc713e0f666.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Matice <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d8c8c636d3f31d64f2c11b723a61ad76.jpg\" style=\"display:block;margin: 0 auto;\" \/> je \u010dtvercov\u00e1 a nav\u00edc symetrick\u00e1. Tyto vlastnosti se n\u00e1m budou hodit d\u00e1le, zapamatujme si je. Matice <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/a0bb9002c1453028bcef0d34dfc23573.jpg\" style=\"display:block;margin: 0 auto;\" \/> m\u00e1 rozm\u011brnost <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/ee3eb39bf58b2fe9c6a5b69b55ff140e.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/0ce2404bd76804e036b1e5a82dabe22a.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Nyn\u00ed je na\u0161\u00edm \u00fakolem spr\u00e1vn\u011b n\u00e1sobit vektory s matic\u00ed a nez\u00edskat \"dva kr\u00e1t dva p\u011bt\", tak\u017ee se soust\u0159ed\u00edme a budeme maxim\u00e1ln\u011b opatrn\u00ed.<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2fc1ec5f4e6ce5cb08d8790149129621.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/b9b27f264a319fb9599597a7fffd1ac9.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/fe86080e1f0ae686df40eda6b67946db.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/281d7e0888baae8417b485f6ccc7630c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Nicm\u00e9n\u011b, m\u00e1me slo\u017eit\u00fd v\u00fdraz! Ve skute\u010dnosti jsme dostali \u010d\u00edslo \u2014 skal\u00e1r. A te\u010f p\u0159ech\u00e1z\u00edme k diferenciaci. Mus\u00edme naj\u00edt derivaci z\u00edskan\u00e9ho v\u00fdrazu podle ka\u017ed\u00e9ho koeficientu <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/b4acde2261a1ef82fdd4bcb851d3d54f.jpg\" style=\"display:block;margin: 0 auto;\" \/> a na v\u00fdstupu dostat vektor s rozm\u011brem <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/9f5b8adf1e914ea3c6181a627b355d40.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Pro jistotu pop\u00ed\u0161u postupy po jednotliv\u00fdch kroc\u00edch:<\/p>\n<p>1) diferencujeme podle <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2522e823e4dee25af7d0268ea467ad75.jpg\" style=\"display:block;margin: 0 auto;\" \/>, dostaneme: <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/7e89620225eaf5e85348ba0f590ecae1.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>2) diferencujeme podle <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/7e5c21598d060f32fee5bd8c46851799.jpg\" style=\"display:block;margin: 0 auto;\" \/>, dostaneme: <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e274a91726e02c61ab075625c10373fa.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>3) diferencujeme podle <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3aab71b33e32b9ce0dee2bcd94c32f14.jpg\" style=\"display:block;margin: 0 auto;\" \/>, dostaneme: <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/abb3d3101af706ea22c98d3cde64dd03.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Na v\u00fdstupu \u2014 sl\u00edben\u00fd vektor o velikosti <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2c50df26519c9627e07598715b132c72.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2312ff08655bffec14f9b969d984ffc2.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Pokud se na vektor pod\u00edv\u00e1te pozorn\u011bji, m\u016f\u017eete si v\u0161imnout, \u017ee lev\u00e9 a odpov\u00eddaj\u00edc\u00ed prav\u00e9 prvky vektoru lze uspo\u0159\u00e1dat tak, \u017ee nakonec z p\u0159edlo\u017een\u00e9ho vektoru m\u016f\u017eeme vy\u010dlenit vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/c0dfe1a9a170f0893dd698aaf9ba9701.jpg\" style=\"display:block;margin: 0 auto;\" \/> velikosti <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/a813524108fffe275a91842c79f8bda8.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Nap\u0159\u00edklad, <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/afdf43758b7923571006e70b1e5de969.jpg\" style=\"display:block;margin: 0 auto;\" \/> (lev\u00fd prvek horn\u00edho \u0159\u00e1dku vektoru) <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/59d90b282c4c6461b19829a1191330d1.jpg\" style=\"display:block;margin: 0 auto;\" \/> (prav\u00fd prvek horn\u00edho \u0159\u00e1dku vektoru) lze p\u0159edstavit jako <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/4b02117662623ab30edd4f1ea7b1be6c.jpg\" style=\"display:block;margin: 0 auto;\" \/>, a <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/219fe99a3a91a27a630bc99feccb3b55.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 jako <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/3179a9d3ec503338de84e5acccc1b4cf.jpg\" style=\"display:block;margin: 0 auto;\" \/> atd. pro ka\u017ed\u00fd \u0159\u00e1dek. Uskup\u00edme:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/07ca35f821e7d5af53d9e0209d007646.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Vyneseme vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/db4e2686a837b8e1c916c267df9faf46.jpg\" style=\"display:block;margin: 0 auto;\" \/> a na v\u00fdstupu dostaneme:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/54e24819b98dd56d38542e64d977a8bb.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Nyn\u00ed se pod\u00edvejme na z\u00edskanou matici. Matice je sou\u010dtem dvou matic <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2676c70f3a1eff48e5fc831a75440194.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/68e49b0efd5cea53f742b7615c77d639.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Vzpomn\u011bli jsme si, \u017ee jsme p\u0159ed chv\u00edl\u00ed zm\u00ednili jednu d\u016fle\u017eitou vlastnost matice <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/78f2e8bc8a9cb907a8317f5859036f71.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 je symetrick\u00e1. Na z\u00e1klad\u011b t\u00e9to vlastnosti m\u016f\u017eeme s jistotou prohl\u00e1sit, \u017ee v\u00fdraz <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/60fe7f4b8c34c3dc15fc7c87eb8aaf61.jpg\" style=\"display:block;margin: 0 auto;\" \/> se rovn\u00e1 <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/65f7e5e232d7e3062e17dfbacc979ea7.jpg\" style=\"display:block;margin: 0 auto;\" \/>. To lze snadno ov\u011b\u0159it, kdy\u017e otev\u0159eme prvek po prvku sou\u010din matic. <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d4684c23eba61d9ddf5b05f59cc5b8f8.jpg\" style=\"display:block;margin: 0 auto;\" \/>Nebudeme to zde d\u011blat, ti, kdo cht\u011bj\u00ed, mohou prov\u00e9st kontrolu sami. <\/p>\n<p>Vr\u00e1t\u00edme se k na\u0161emu v\u00fdrazu. Po na\u0161ich transformac\u00edch vypad\u00e1 tak, jak jsme cht\u011bli, aby vypadal:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/01349d32efab108cc0208b4ff732f5b4.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Tak\u017ee prvn\u00edho diferenciov\u00e1n\u00ed jsme se \u00fasp\u011b\u0161n\u011b zhostili. P\u0159ech\u00e1z\u00edme k druh\u00e9mu v\u00fdrazu.<\/p>\n<h3>Diferencov\u00e1n\u00ed 2<\/h3>\n<p>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/5774072b36c83a305fd525b0fdffd59b.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>P\u016fjdeme po vy\u0161lapan\u00e9 cest\u011b. Bude mnohem krat\u0161\u00ed ne\u017e ta p\u0159edchoz\u00ed, tak\u017ee se ned\u00e1vejte p\u0159\u00edli\u0161 daleko od obrazovky.<\/p>\n<p>Rozlo\u017e\u00edme po jednotliv\u00fdch prvc\u00edch vektory a matici:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d6f1f2520c683c34c93947fdc1d74c7d.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/a15e0b5d35596a2eb210d4467426ebda.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/6f4f7ebd2f1e9cfa5d5f96c1b5298c3a.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Na chv\u00edli odstran\u00edme ze v\u00fdpo\u010dt\u016f dvojku \u2014 ta zde nehraje \u017e\u00e1dnou roli, pak ji vr\u00e1t\u00edme na m\u00edsto. Vyn\u00e1sob\u00edme vektory matic\u00ed. Nejd\u0159\u00edve vyn\u00e1sob\u00edme matici <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/8f09bef67ae021b46e878b4ae32e122d.jpg\" style=\"display:block;margin: 0 auto;\" \/> vektorem <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/1db14935f79198aebd01b753ff3b697b.jpg\" style=\"display:block;margin: 0 auto;\" \/>, zde nem\u00e1me \u017e\u00e1dn\u00e1 omezen\u00ed. Dostaneme vektor velikosti <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/a962a34aa48787f3a5befd3bbfd0ed8c.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/5612d20b4c5523cf0e34c409ba424d0e.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Provedeme dal\u0161\u00ed akci \u2014 vyn\u00e1sob\u00edme vektor <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/6b8566eabdfe892618ca9c26a9ac4faf.jpg\" style=\"display:block;margin: 0 auto;\" \/> p\u0159ijat\u00fdm vektorem. Na v\u00fdstupu n\u00e1s \u010dek\u00e1 \u010d\u00edslo:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/50698c81b18f0273550fdf34ba6626fd.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>To je to, co budeme diferencovat. Na v\u00fdstupu z\u00edsk\u00e1me vektor dimenze <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/73a13a4ef020e6d67551dd2dd66544e0.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/d63b2486e7186c4a7e11d21a769c0aa5.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>N\u011bco v\u00e1m to p\u0159ipom\u00edn\u00e1? Spr\u00e1vn\u011b! To je sou\u010din matice <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/67146a714d3889b5e9fcaf19e7e2407d.jpg\" style=\"display:block;margin: 0 auto;\" \/> vektorem <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/8c3e90abfd5f687c1b5852980c65b0a8.jpg\" style=\"display:block;margin: 0 auto;\" \/>. <\/p>\n<p>T\u00edmto zp\u016fsobem jsme \u00fasp\u011b\u0161n\u011b dokon\u010dili druh\u00e9 diferenciov\u00e1n\u00ed.<\/p>\n<h2>Na z\u00e1v\u011br<\/h2>\n<p>\nNyn\u00ed v\u00edme, jak vzniklo rovnost <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/8dd8f1dae6629da173b7e71f569a18a1.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p>Nakonec pop\u00ed\u0161eme rychlou cestu transformac\u00ed z\u00e1kladn\u00edch vzorc\u016f.<\/p>\n<p><b>Odhadneme kvalitu modelu podle metody nejmen\u0161\u00edch \u010dtverc\u016f:<\/b><br \/>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/e4f1216018252f75c89bb283dbd165c0.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/18c71ca2156610ab70a7776e0d660560.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><b>Diferencujeme z\u00edskan\u00fd v\u00fdraz:<\/b><br \/>\n<img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/ef0989a3750d444845d96cd7b4c26568.jpg\" style=\"display:block;margin: 0 auto;\" \/> <img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/2f0788dce58d900c2b11b826943785fb.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><img decoding=\"async\" alt=\"P\u0159ev\u00e1d\u00edme rovnici line\u00e1rn\u00ed regrese do maticov\u00e9ho tvaru\" src=\"\/wp-content\/uploads\/2019\/12\/fc6183460bbf00ef4c040502055e032a.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<h2>Literatura<\/h2>\n<p>\n<u><b>Internetov\u00e9 zdroje:<\/b><\/u><\/p>\n<p>1) <i><noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/278513\/\">habr.com\/ru\/post\/278513<\/a><\/noindex><\/i><br \/>\n2) <i><noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/company\/ods\/blog\/322076\/\">habr.com\/ru\/company\/ods\/blog\/322076<\/a><\/noindex><\/i><br \/>\n3) <i><noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/307004\/\">habr.com\/ru\/post\/307004<\/a><\/noindex><\/i><br \/>\n4) <i><noindex><a rel=\"nofollow\" href=\"http:\/\/nabatchikov.com\/blog\/view\/matrix_der\">nabatchikov.com\/blog\/view\/matrix_der<\/a><\/noindex><\/i><\/p>\n<p><u><b>U\u010debnice, sborn\u00edky \u00faloh:<\/b><\/u><\/p>\n<p>1) Konspekt p\u0159edn\u00e1\u0161ek z vy\u0161\u0161\u00ed matematiky: kompletn\u00ed kurz \/ D.T. P\u00edsmen\u00fd \u2013 4. vyd. \u2013 M.: Iris-press, 2006<br \/>\n2) Aplikovan\u00e1 regrese \/ N. Draper, G. Smith \u2013 2. vyd. \u2013 M.: Finance a statistika, 1986 (p\u0159eklad z angli\u010dtiny)<br \/>\n3) \u00dalohy na \u0159e\u0161en\u00ed maticov\u00fdch rovnic: <br \/>\n<i><noindex><a rel=\"nofollow\" href=\"https:\/\/function-x.ru\/matrix_equations.html\">function-x.ru\/matrix_equations.html<\/a><\/noindex><br \/>\n<noindex><a rel=\"nofollow\" href=\"http:\/\/mathprofi.ru\/deistviya_s_matricami.html\">mathprofi.ru\/deistviya_s_matricami.html<\/a><\/noindex><\/i><br \/>\n<br \/>Zdroj: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/479398\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u0426\u0435\u043b\u044c \u0441\u0442\u0430\u0442\u044c\u0438 \u2014 \u043e\u043a\u0430\u0437\u0430\u043d\u0438\u0435 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0438 \u043d\u0430\u0447\u0438\u043d\u0430\u044e\u0449\u0438\u043c \u0434\u0430\u0442\u0430\u0441\u0430\u0439\u043d\u0442\u0438\u0441\u0442\u0430\u043c. \u0412 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043d\u0430 \u043f\u0430\u043b\u044c\u0446\u0430\u0445 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438 \u0442\u0440\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438: \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435, \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u044b\u0439 \u0441\u043f\u0443\u0441\u043a, \u0441\u0442\u043e\u0445\u0430\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u044b\u0439 \u0441\u043f\u0443\u0441\u043a. \u0422\u043e\u0433\u0434\u0430 \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043b\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 . \u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435, \u043a\u0430\u043a \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0438\u0437 \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0430, \u043c\u044b \u043e\u0431\u043e\u0441\u043d\u0443\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0438\u043b\u0438 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u044c\u043d\u043e \u0435\u0435 \u0432\u044b\u0432\u0435\u0434\u0435\u043c. \u041f\u043e\u0447\u0435\u043c\u0443 \u0438\u043c\u0435\u0435\u0442 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-53777","post","type-post","status-publish","format-standard","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.3 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u0426\u0435\u043b\u044c \u0441\u0442\u0430\u0442\u044c\u0438 \u2014 \u043e\u043a\u0430\u0437\u0430\u043d\u0438\u0435 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0438.\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"Yuri Gagarin\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/prohoster.info\/cs\/blog\/news\/privodim-uravnenie-linejnoj-regressii-v-matrichnyj-vid\" \/>\n\t\t<meta name=\"generator\" 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