{"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\/sq\/blog\/news\/privodim-uravnenie-linejnoj-regressii-v-matrichnyj-vid","title":{"rendered":"Shprehim ekuacionin e regresionit linear n\u00eb form\u00eb matricore","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"Shprehim
\n
\nQ\u00ebllimi i artikullit \u00ebsht\u00eb t\u00eb mb\u00ebshtes\u00eb fillestar\u00ebt n\u00eb datascience. artikulli i m\u00ebparsh\u00ebm<\/a><\/noindex> Ne e shqyrtuam n\u00eb m\u00ebnyr\u00eb t\u00eb thjesht\u00eb tri m\u00ebnyra p\u00ebr t\u00eb zgjidhur ekuacionin e regresionit linear: zgjidhje analitike, zbritje gradiente, zbritje gradiente stohastike. At\u00ebher\u00eb, p\u00ebr zgjidhjen analitike, aplikuam formul\u00ebn \"Shprehim. N\u00eb k\u00ebt\u00eb artikull, si\u00e7 del nga titulli, ne do t\u00eb justifikojm\u00eb p\u00ebrdorimin e k\u00ebsaj formule ose, me fjal\u00eb t\u00eb tjera, do ta nxjerrim vet\u00eb. <\/p>\n

Pse ka kuptim t\u00eb kushtojm\u00eb v\u00ebmendje t\u00eb shtuar formul\u00ebs \"Shprehim? <\/p>\n

Pik\u00ebrisht nga ekuacioni matricor zakonisht fillon njohja me regresionin linear. Nd\u00ebrkoh\u00eb, zgjidhjet e detajuar se si \u00ebsht\u00eb nxjerr\u00eb formula ndodhin rrall\u00eb.
\n<\/a><\/noindex>
\nP\u00ebr shembull, n\u00eb kurset mbi m\u00ebsimin e makinerive n\u00eb Yandex, kur audienca njihet me regularizimin, ofrohet p\u00ebrdorimi i funksioneve nga biblioteka sklearn<\/i>, nd\u00ebrkoh\u00eb q\u00eb nuk p\u00ebrmendet asnj\u00eb fjal\u00eb p\u00ebr p\u00ebrfaq\u00ebsimin matricor t\u00eb algoritmit. Pik\u00ebrisht n\u00eb k\u00ebt\u00eb moment, disa d\u00ebshira mund t\u00eb shfaqen tek disa nga t\u00eb pranishmit q\u00eb t\u00eb hedhin nj\u00eb v\u00ebshtrim m\u00eb t\u00eb thell\u00eb n\u00eb k\u00ebt\u00eb \u00e7\u00ebshtje \u2014 t\u00eb shkruajn\u00eb kod pa p\u00ebrdorur funksione t\u00eb gatshme. Dhe p\u00ebr k\u00ebt\u00eb, s\u00eb pari, duhet t\u00eb paraqesim ekuacionin me regularizuesin n\u00eb form\u00eb matricore. Ky artikull, pik\u00ebrisht, do t\u00eb ndihmoj\u00eb ata q\u00eb d\u00ebshirojn\u00eb t\u00eb zot\u00ebrojn\u00eb k\u00ebto aft\u00ebsi. Le t\u00eb fillojm\u00eb.<\/p>\n

Kushtet fillestare<\/h2>\n

<\/p>\n

T\u00eb dh\u00ebnat e targetit<\/h3>\n

\nNe kemi nj\u00eb seri vlerash p\u00ebr treguesin e synuar. P\u00ebr shembull, treguesi i synuar mund t\u00eb jet\u00eb \u00e7mimi i ndonj\u00eb aktivi: naft\u00eb, ar, grur\u00eb, dollar etj. Nd\u00ebrkoh\u00eb, me nj\u00eb seri vlerash t\u00eb treguesit t\u00eb synuar kuptojm\u00eb numrin e v\u00ebzhgimeve. T\u00eb tilla v\u00ebzhgime mund t\u00eb jen\u00eb, p\u00ebr shembull, \u00e7mimet mujore t\u00eb naft\u00ebs p\u00ebr nj\u00eb vit, pra do t\u00eb kemi 12 vlera t\u00eb treguesit t\u00eb synuar. Le t\u00eb fillojm\u00eb t\u00eb vendosim shenjat. Do t\u00eb shenojm\u00eb \u00e7do vler\u00eb t\u00eb treguesit t\u00eb synuar si \"Shprehim. N\u00eb total kemi \"Shprehim v\u00ebzhgime, prandaj mund ta paraqesim v\u00ebzhgimin ton\u00eb si \"Shprehim.<\/p>\n

Regresor\u00ebt<\/h3>\n

\nDo t\u00eb mendojm\u00eb se ekzistojn\u00eb faktor\u00eb q\u00eb, n\u00eb nj\u00eb far\u00eb mase, shpjegojn\u00eb vlerat e treguesit t\u00eb synuar. P\u00ebr shembull, n\u00eb kursin e \u00e7iftit dollar\/rupie, \u00e7mimi i naft\u00ebs, niveli i FRS-s\u00eb, dhe t\u00eb tjer\u00eb kan\u00eb nj\u00eb ndikim t\u00eb fort\u00eb. T\u00eb till\u00eb faktor\u00eb quhen regresor\u00eb. N\u00eb t\u00eb nj\u00ebjt\u00ebn koh\u00eb, \u00e7do vler\u00eb e treguesit t\u00eb synuar duhet t\u00eb p\u00ebrputhet me nj\u00eb vler\u00eb regresori, dometh\u00ebn\u00eb, n\u00ebse kemi 12 tregues t\u00eb synuar p\u00ebr \u00e7do muaj t\u00eb vitit 2018, at\u00ebher\u00eb do t\u00eb kemi gjithashtu 12 vlera regresor\u00ebsh p\u00ebr t\u00eb nj\u00ebjtin periudh\u00eb. Le t\u00eb sh\u00ebnojm\u00eb vlerat e secilit regresor me \"Shprehim. Le t\u00eb supozojm\u00eb se n\u00eb rastin ton\u00eb ka \"Shprehim regresor\u00eb (dmth, \"Shprehim faktor\u00eb q\u00eb ndikojn\u00eb n\u00eb vlerat e treguesit t\u00eb synuar). K\u00ebshtu, regresor\u00ebt tan\u00eb mund t\u00eb paraqiten si m\u00eb posht\u00eb: p\u00ebr regresorin 1 (p.sh., \u00e7mimi i naft\u00ebs): \"Shprehim, p\u00ebr regresorin 2 (p.sh., niveli i FRS-s\u00eb): \"Shprehim, p\u00ebr «\"Shprehim-t\u00eb» regresorit: \"Shprehim<\/p>\n

Var\u00ebsia e treguesve t\u00eb synuar nga regresor\u00ebt<\/h3>\n

\nSupozoni se var\u00ebsia e treguesit t\u00eb synuar \"Shprehim nga regresor\u00ebt «\"Shprehim-t\u00eb» v\u00ebzhgimit mund t\u00eb shprehet p\u00ebrmes ekuacionit t\u00eb regresionit linear:<\/p>\n

\"Shprehim<\/p>\n

index \"Shprehim \u2014 «\"Shprehim-ta» vlera e regresorit nga 1 n\u00eb \"Shprehim,<\/p>\n

\"Shprehim \u2014 numri i regresor\u00ebve nga 1 deri n\u00eb \"Shprehim<\/p>\n

\"Shprehim \u2014 koeficient\u00ebt k\u00ebndor\u00eb, t\u00eb cil\u00ebt p\u00ebrfaq\u00ebsojn\u00eb madh\u00ebsin\u00eb me t\u00eb cil\u00ebn do t\u00eb ndryshoj\u00eb treguesi i propozuar n\u00eb mesatare me ndryshimin e regresorit. <\/p>\n

Me fjal\u00eb t\u00eb tjera, p\u00ebr secilin (p\u00ebrve\u00e7 \"Shprehim) regresor p\u00ebrcaktojm\u00eb \"koeficientin\" ton\u00eb t\u00eb ve\u00e7ant\u00eb \"Shprehim, pastaj shum\u00ebzojm\u00eb koeficient\u00ebt me vlerat e regresor\u00ebve «\"Shprehim-t\u00eb» v\u00ebzhgimit, si rezultat marrim nj\u00eb af\u00ebrsi «\"Shprehim-t\u00eb» treguesit t\u00eb synuar.<\/p>\n

Prandaj, na nevojitet t\u00eb p\u00ebrshtatim koeficient\u00eb t\u00eb till\u00eb \"Shprehim, p\u00ebr t\u00eb cil\u00ebt vlerat e funksionit ton\u00eb aproksimues \"Shprehim do t\u00eb jen\u00eb sa m\u00eb af\u00ebr vlerave t\u00eb treguesve t\u00eb synuar.<\/p>\n

Vler\u00ebsimi i cil\u00ebsis\u00eb s\u00eb funksionit aproksimues<\/h3>\n

\nDo t\u00eb p\u00ebrcaktojm\u00eb vler\u00ebsimin e cil\u00ebsis\u00eb s\u00eb funksionit aproksimues me metod\u00ebn e katror\u00ebve t\u00eb vegj\u00ebl. Funksioni i vler\u00ebsimit t\u00eb cil\u00ebsis\u00eb n\u00eb k\u00ebt\u00eb rast do t\u00eb marr\u00eb form\u00ebn e m\u00ebposhtme:<\/p>\n

\"Shprehim<\/p>\n

Na nevojitet t\u00eb p\u00ebrshtatim vlera t\u00eb tilla t\u00eb koeficient\u00ebve $w$, p\u00ebr t\u00eb cilat vlera \"Shprehim do t\u00eb jet\u00eb sa m\u00eb e vog\u00ebl.<\/p>\n

Kthejm\u00eb ekuacionin n\u00eb form\u00eb matricore<\/h2>\n

<\/p>\n

P\u00ebrfaq\u00ebsimi vektor<\/h3>\n

\nP\u00ebr shkak se t\u00eb fillojm\u00eb, p\u00ebr ta b\u00ebr\u00eb jet\u00ebn m\u00eb t\u00eb leht\u00eb, duhet t\u00eb p\u00ebrqendrohemi n\u00eb ekuacionin e regresionit linear dhe t\u00eb v\u00ebrejm\u00eb se koeficienti i par\u00eb \"Shprehim nuk e mnohet me asnj\u00eb regresor. Megjithat\u00eb, kur t\u2019i shnd\u00ebrrojm\u00eb t\u00eb dh\u00ebnat n\u00eb form\u00ebn matricore, rasti i m\u00ebsip\u00ebrm do t\u00eb nd\u00ebrlikoj\u00eb seriozisht llogaritjet. Prandaj, propozohet t\u00eb vendosim nj\u00eb regresor tjet\u00ebr p\u00ebr koeficientin e par\u00eb. \"Shprehim dhe ta barazojm\u00eb me nj\u00eb. N\u00eb fakt, \u00e7do «\"Shprehim-ta» vler\u00eb e k\u00ebtij regresori ta barazojm\u00eb me nj\u00eb - sepse duke shum\u00ebzuar me nj\u00eb, nga aspekti i rezultateve t\u00eb llogaritjeve nuk do t\u00eb ket\u00eb asnj\u00eb ndryshim, por nga aspekti i rregullave t\u00eb mnoz\u00ebs s\u00eb matriceve, do t\u00eb kemi shum\u00eb m\u00eb pak pun\u00eb. <\/p>\n

Tani, p\u00ebr nj\u00eb koh\u00eb, p\u00ebr q\u00ebllim t\u00eb thjesht\u00ebsimit t\u00eb materialit, le t\u00eb supozojm\u00eb se kemi vet\u00ebm nj\u00eb «\"Shprehim-t\u00eb» v\u00ebzhgim. At\u00ebher\u00eb, le t\u00eb paraqesim vlerat e regresor\u00ebve «\"Shprehim-t\u00eb» v\u00ebzhgimit si nj\u00eb vektor \"Shprehim. Vektori \"Shprehim ka dimension \"Shprehim, q\u00eb do t\u00eb thot\u00eb \"Shprehim rreshta dhe 1 kolon\u00eb:<\/p>\n

\"Shprehim<\/p>\n

Koeficient\u00ebt e k\u00ebrkuar le t\u00eb paraqiten si nj\u00eb vektor \"Shprehim, i cili ka dimension \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

Ekuacioni i regresionit linear p\u00ebr «\"Shprehim-t\u00eb» v\u00ebzhgimit do t\u00eb ket\u00eb k\u00ebt\u00eb form\u00eb: <\/p>\n

\"Shprehim<\/p>\n

Funksioni i vler\u00ebsimit t\u00eb cil\u00ebsis\u00eb s\u00eb modelit linear do t\u00eb jet\u00eb:<\/p>\n

\"Shprehim<\/p>\n

V\u00ebmendje, sipas rregullave t\u00eb mnohimit t\u00eb matricave, duhet t\u00eb transponojm\u00eb vektorin \"Shprehim.<\/p>\n

Prezantimi matricor<\/h3>\n

\nSi rezultat i mnohimit t\u00eb vektor\u00ebve, do t\u00eb marrim nj\u00eb num\u00ebr: \"Shprehim, si\u00e7 pritej. Ky num\u00ebr \u00ebsht\u00eb af\u00ebrsia «\"Shprehim-t\u00eb» treguesit t\u00eb synuar. Por ne kemi nevoj\u00eb p\u00ebr af\u00ebrsit\u00eb jo vet\u00ebm p\u00ebr nj\u00eb vler\u00eb t\u00eb treguesit t\u00eb synuar, por p\u00ebr t\u00eb gjitha. P\u00ebr k\u00ebt\u00eb, le t\u00eb shkruajm\u00eb t\u00eb gjith\u00eb «\"Shprehim-t\u00eb» regresor\u00ebt n\u00eb formatin e matric\u00ebs. \"ShprehimMatrica e marr\u00eb ka dimension \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

Tani, ekvivalenti i regresionit linear do t\u00eb marr\u00eb form\u00ebn:<\/p>\n

\"Shprehim<\/p>\n

Le t\u00eb em\u00ebrtojm\u00eb vlerat e treguesve t\u00eb synuar (t\u00eb gjitha \"Shprehim) si nj\u00eb vektor \"Shprehim me dimension \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

Tani mund t\u00eb shkruajm\u00eb n\u00eb format matricor ekvacionin e vler\u00ebsimit t\u00eb cil\u00ebsis\u00eb s\u00eb modelit linear:<\/p>\n

\"Shprehim<\/p>\n

Praktikisht, nga kjo formul\u00eb do t\u00eb merrni formul\u00ebn e njohur \"Shprehim<\/p>\n

Si b\u00ebhet kjo? Hapim zarfet, kryejm\u00eb diferenciimin, transformojm\u00eb shprehjet e marra, etj., dhe pik\u00ebrisht me k\u00ebt\u00eb ne do t\u00eb merremi tani.<\/p>\n

Transformimet matricore<\/h2>\n

<\/p>\n

Hapim zarfet<\/h3>\n

\n\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

P\u00ebrgatitim ekvacionin p\u00ebr diferenciim<\/h3>\n

\nP\u00ebr k\u00ebt\u00eb do t\u00eb kryejm\u00eb disa transformime. N\u00eb llogaritjet e m\u00ebvonshme do t\u00eb jet\u00eb m\u00eb e leht\u00eb n\u00ebse vektori \"Shprehim do t\u00eb paraqitet n\u00eb fillim t\u00eb \u00e7do produkti n\u00eb ekuacion.<\/p>\n

Transformimi 1<\/h4>\n

\n\"Shprehim<\/p>\n

Si e ndodhi deri k\u00ebtu? P\u00ebr t\u00eb p\u00ebrgjigjur k\u00ebt\u00eb pyetje, mjafton t\u00eb shikojm\u00eb dimensionet e matriceve t\u00eb shumzuara dhe t\u00eb shohim se n\u00eb fund marrim nj\u00eb num\u00ebr ose ndryshe \"Shprehim.<\/p>\n

Le t\u00eb shkruajm\u00eb dimensionet e shprehjeve matricore.<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

Transformimi 2<\/h4>\n

\n\"Shprehim<\/p>\n

T\u00eb shkruajm\u00eb nj\u00ebsoj si n\u00eb transformimin 1<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

N\u00eb daljen kemi nj\u00eb ekuacion, t\u00eb cilin na duhet ta diferencojm\u00eb:
\n\"Shprehim<\/p>\n

Diferencojm\u00eb funksionin e vler\u00ebsimit t\u00eb cil\u00ebsis\u00eb s\u00eb modelit<\/h2>\n

\nT\u00eb diferencojm\u00eb sipas vektorit \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

\n\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

Nuk duhet t\u00eb ket\u00eb pyetje pse \"Shprehim por operacionet p\u00ebr p\u00ebrcaktimin e derivatave n\u00eb dy shprehje t\u00eb tjera do t'i shqyrtojm\u00eb m\u00eb n\u00eb detaje.<\/p>\n

Diferencimi 1<\/h3>\n

\nT\u00eb hapim diferencimin: \"Shprehim<\/p>\n

P\u00ebr t\u00eb p\u00ebrcaktuar derivat\u00ebn e nj\u00eb matrice ose vektori, duhet t\u00eb shikojm\u00eb se \u00e7far\u00eb kan\u00eb brenda. Shikojm\u00eb:<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim \"Shprehim<\/p>\n

Le t\u00eb sh\u00ebnojm\u00eb produktin e matricave \"Shprehim p\u00ebrmes matrices \"Shprehim. Matrica \"Shprehim \u00ebsht\u00eb katrore dhe m\u00eb tep\u00ebr, ajo \u00ebsht\u00eb simetrike. K\u00ebto prop\u00ebrt\u00ebsi do na nevojiten m\u00eb von\u00eb, le t\u00eb kujtojm\u00eb ato. Matrica \"Shprehim ka dimension \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

Tani detyra jon\u00eb \u00ebsht\u00eb t\u00eb shumzojm\u00eb sakt\u00eb vektor\u00ebt me matric\u00ebn dhe t\u00eb mos marr\u00eb shprehje t\u00eb gabuara, k\u00ebshtu q\u00eb do t\u00eb p\u00ebrqendrohemi dhe do t\u00eb jemi shum\u00eb t\u00eb kujdessh\u00ebm.<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

Megjithat\u00eb, duke e par\u00eb mir\u00eb shprehjen e komplikuar q\u00eb kemi, n\u00eb t\u00eb v\u00ebrtet\u00eb kemi marr\u00eb nj\u00eb num\u00ebr \u2014 skalar. Tani, me t\u00eb v\u00ebrtet\u00eb, kalojm\u00eb n\u00eb diferencimin. Duhet t\u00eb gjejm\u00eb derivat\u00ebn e shprehjes s\u00eb marr\u00eb sipas \u00e7do koeficienti \"Shprehim dhe t\u00eb marrim si rezultat nj\u00eb vektor me dimension \"Shprehim. P\u00ebr \u00e7do rast, do ta p\u00ebrshkruaj procedur\u00ebn e veprimeve:<\/p>\n

1) do t\u00eb diferencojm\u00eb sipas \"Shprehim, do t\u00eb marrim: \"Shprehim<\/p>\n

2) do t\u00eb diferencojm\u00eb sipas \"Shprehim, do t\u00eb marrim: \"Shprehim<\/p>\n

3) do t\u00eb diferencojm\u00eb sipas \"Shprehim, do t\u00eb marrim: \"Shprehim<\/p>\n

N\u00eb daljen \u2014 vektori i premtuar me p\u00ebrmas\u00eb \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

N\u00ebse e shikoni vektorin me kujdes, mund t\u00eb vini re se elementet e majta dhe ato t\u00eb djathta t\u00eb p\u00ebrputhura n\u00eb vektor mund t\u00eb grupohen n\u00eb m\u00ebnyr\u00eb q\u00eb n\u00eb fund nga vektori i paraqitur t\u00eb nxjerrim vektorin \"Shprehim me p\u00ebrmas\u00eb \"Shprehim. P\u00ebr shembull, \"Shprehim (elementi i majt\u00eb i rreshtit t\u00eb sip\u00ebrm t\u00eb vektorit) \"Shprehim (elementi i djatht\u00eb i rreshtit t\u00eb sip\u00ebrm t\u00eb vektorit) mund t\u00eb paraqitet si \"Shprehim, nd\u00ebrsa \"Shprehim \u2014 si \"Shprehim e k\u00ebshtu me radh\u00eb p\u00ebr \u00e7do rresht. Le t\u00eb grupojm\u00eb:<\/p>\n

\"Shprehim<\/p>\n

T\u00eb nxjerrim vektorin \"Shprehim dhe n\u00eb dalje do t\u00eb marr\u00eb:<\/p>\n

\"Shprehim<\/p>\n

Tani, le t\u00eb shikojm\u00eb matric\u00ebn e marr\u00eb. Matrica p\u00ebrb\u00ebn shum\u00ebn e dy matricave \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

Kujtojm\u00eb se disa her\u00eb m\u00eb par\u00eb, ne theksuam nj\u00eb pron\u00eb t\u00eb r\u00ebnd\u00ebsishme t\u00eb matric\u00ebs \"Shprehim \u2014 ajo \u00ebsht\u00eb simetrike. Duke u bazuar n\u00eb k\u00ebt\u00eb pron\u00eb, ne mund t\u00eb themi me besim se shprehja \"Shprehim \u00ebsht\u00eb e barabart\u00eb me \"Shprehim. Kjo \u00ebsht\u00eb e leht\u00eb p\u00ebr t'u verifikuar, duke hapur produktin e matricave element p\u00ebr element. \"Shprehim. Nuk do ta b\u00ebjm\u00eb k\u00ebt\u00eb k\u00ebtu, ata q\u00eb jan\u00eb t\u00eb interesuar mund ta kontrollojn\u00eb vet\u00eb. <\/p>\n

T\u00eb kthehemi te shprehja jon\u00eb. Pas transformimeve tona, ajo doli ashtu si\u00e7 do ta d\u00ebshironim ta shihnim:<\/p>\n

\"Shprehim<\/p>\n

K\u00ebshtu, ne e p\u00ebrfunduam diferencimin e par\u00eb. Kalojm\u00eb te shprehja e dyt\u00eb.<\/p>\n

Diferencimi 2<\/h3>\n

\n\"Shprehim<\/p>\n

T\u00eb shkojm\u00eb n\u00ebp\u00ebr rrug\u00ebn e shtruar. Ajo do t\u00eb jet\u00eb shum\u00eb m\u00eb e shkurt\u00ebr se e para, k\u00ebshtu q\u00eb mos u largoni shum\u00eb nga ekrani.<\/p>\n

T\u00eb hapim elementet e vektor\u00ebve dhe matric\u00ebs:<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

P\u00ebr momentin, do ta heqim numrin dy nga llogaritjet \u2014 ai nuk luan nj\u00eb rol t\u00eb madh, m\u00eb von\u00eb do ta kthejm\u00eb p\u00ebrs\u00ebri. Do t'i shum\u00ebzojm\u00eb vektor\u00ebt me matric\u00ebn. S\u00eb pari do ta shum\u00ebzojm\u00eb matric\u00ebn \"Shprehim me vektor \"Shprehim, k\u00ebtu nuk kemi ndonj\u00eb kufizim. Do t\u00eb marrim nj\u00eb vektor me p\u00ebrmas\u00eb \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

T\u00eb kryejm\u00eb veprimin e m\u00ebpassh\u00ebm \u2014 do ta shum\u00ebzojm\u00eb vektor \"Shprehim me vektorin e marr\u00eb. N\u00ebfund do t\u00eb na pres\u00eb nj\u00eb num\u00ebr:<\/p>\n

\"Shprehim<\/p>\n

At\u00eb do ta diferencojm\u00eb. N\u00ebfund do t\u00eb marim nj\u00eb vektor me dimension \"Shprehim:<\/p>\n

\"Shprehim<\/p>\n

K\u00ebtu ka di\u00e7ka q\u00eb t\u00eb kujton? E sakt\u00eb! Kjo \u00ebsht\u00eb shumimi i matric\u00ebs \"Shprehim me vektor \"Shprehim. <\/p>\n

K\u00ebshtu, diferencimi i dyt\u00eb p\u00ebrfundoi me sukses.<\/p>\n

N\u00eb p\u00ebrfundim<\/h2>\n

\nTani e dim\u00eb si doli barazia \"Shprehim.<\/p>\n

N\u00eb fund, do t\u00eb p\u00ebrshkruajm\u00eb nj\u00eb rrug\u00eb t\u00eb shpejt\u00eb t\u00eb transformimeve t\u00eb formulave kryesore.<\/p>\n

Do ta vler\u00ebsojm\u00eb cil\u00ebsin\u00eb e modelit sipas metod\u00ebs s\u00eb katror\u00ebve m\u00eb t\u00eb vegj\u00ebl:<\/b>
\n\"Shprehim<\/p>\n

\"Shprehim<\/p>\n

Do t\u00eb diferencojm\u00eb shprehjen e marr\u00eb:<\/b>
\n\"Shprehim \"Shprehim<\/p>\n

\"Shprehim<\/p>\n

Literatura<\/h2>\n

\nBurimet n\u00eb internet:<\/b><\/u><\/p>\n

1) habr.com\/ru\/post\/278513<\/a><\/noindex><\/i>
\n2) habr.com\/ru\/company\/ods\/blog\/322076<\/a><\/noindex><\/i>
\n3) habr.com\/ru\/post\/307004<\/a><\/noindex><\/i>
\n4) nabatchikov.com\/blog\/view\/matrix_der<\/a><\/noindex><\/i><\/p>\n

Libra, koleksione ushtrimesh:<\/b><\/u><\/p>\n

1) Sh\u00ebnime t\u00eb leksioneve p\u00ebr matematik\u00ebn e lart\u00eb: kurs i plot\u00eb \/ D.T. Pismennyi \u2013 Botimi i 4-t\u00eb \u2013 M.: Airis-press, 2006
\n2) Analiza regresive e aplikuar \/ N. Draper, G. Smith \u2013 Botimi i 2-t\u00eb \u2013 M.: Financat dhe statistika, 1986 (p\u00ebrkthim nga anglishtja)
\n3) Problemet p\u00ebr zgjidhjen e ekuacioneve matricore:
\nfunction-x.ru\/matrix_equations.html<\/a><\/noindex>
\nmathprofi.ru\/deistviya_s_matricami.html<\/a><\/noindex><\/i>
\n
Burimi: habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

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