Ilmin Lissafi matrix. matrix multiplication

More zamanin da na Sin lissafi amfani da su ƙidãyar post a tabular form tare da wani yawan layuka da kuma ginshikan. Sa'an nan, kamar ilmin lissafi abubuwa kira a matsayin "sihiri square". Ko da yake a san lokuta na yin amfani da allunan a cikin nau'i na triangles, wanda ba a yadu soma.

Don kwanan wata, a ilmin lissafi matrix fiye gane obokt rectangular siffar da qaddara yawan ginshikan da kuma alamomin da cewa ayyana girma na matrix. A lissafi, wani nau'i na rikodi da aka yadu amfani da rikodin a wani m nau'i na bambanci tsarin, kazalika da na mikakke algebraic lissafai. An zaci cewa yawan layuka a cikin matrix daidaita da adadin ba a cikin tsarin na lissafai, yawan ginshikan yayi dace da nawa da ba a sani ba dole ne a tsare a cikin shakka daga cikin bayani.

Bayan da cewa matrix kanta a cikin shakka daga ta bayani kaiwa zuwa gano da ba a sani ba muhimmi a cikin yanayin da tsarin, akwai wani yawan algebraic ayyukan da ake halatta kawo a kan wani ba ilmin lissafi abu. Wannan jerin hada Bugu da kari na matrices da ciwon guda girma. A multiplication na matrices tare dace girma (da shi ne zai yiwu a ninka a matrix da daya gefen ciwon yawan ginshikan daidaita da yawan layuka na matrix a daya gefen). Haka kuma an yarda ninka a matrix da wani vector, ko wani kashi ko tushe zobe (in ba haka ba scalar).

Idan akai la'akari da matrix multiplication dole ne a cigaba da sanya idanu ga tsananin farko yawan ginshikan daidaita da yawan layuka na biyu. In ba haka ba, da mataki na matrix ba a bayyana. Bisa ga doka, da wadda ta matrix-matrix multiplication, kowane kashi a cikin sabon tsararru daidai da Naira Miliyan Xari da kayayyakin da m abubuwa daga cikin layuka na farko matrix abubuwa daga wasu ginshikan.

Domin tsabta, bari mu duba wani misali na yadda matrix multiplication faruwa. Ɗauki matrix A

Fabrairu 3 -2

3 4 0

-1 2 -2,

ninka shi da matrix B

3 -2

1 0

4 -3.

A kashi na farko jere na farko shafi na sakamakon matrix ne daidai da 2 * 3 + 3 * 1 + (- 2) * 4. Haka kuma, a cikin farkon jere a karo na biyu shafi kashi zai daidaita 2 * (- 2) + 3 * 0 + (- 2) * (- 3), kuma haka a har ciko na kowane kashi na sabon matrix. Rule matrix multiplication shafi cewa sakamakon samfurin mxn matrix sigogi da matrix da ciwon wani rabo nxk, zama a teburin wanda yana da girman m x k. Bayan wannan mulkin, za mu iya cewa da samfurin na da ake kira square matrices, bi da bi, daga cikin guda domin an ko da yaushe a tsare.

Daga da kaddarorin mallaki by matrix multiplication ya kamata a kasaftawa a matsayin asali cewa wannan aiki ne ba zabi. Wannan ne samfurin na matrix M to N ba ta daidaita da samfurin na N ta M. Idan a square matrices daga cikin wannan tsari ne ya lura da cewa su a gaba da kuma baya samfurin da aka yaushe m, dabam-dabam ne kawai a sakamakon haka, rectangular matrix kamar wasu yanayi da ake ba ko da yaushe ya cika.

A matrix multiplication akwai wani yawan Properties cewa suna da wata hujja ilmin lissafi bayyanannu. Associativity multiplying nufin aminci wadannan ilmin lissafi magana: (MN) K = M (NK), inda M, N, da kuma K - a matrix da ciwon da sigogi a wadda multiplication aka bayyana. Distributivity multiplication kwakwalwa gaba da cewa M (N + K) = MN + MK, (M + N) K = MK + NK, L (MN) = (LM) N + M (LN), inda L - lambar.

A sakamakon da kaddarorin na matrix multiplication, da ake kira "associative", shi ya bi da cewa a wani samfurin dauke da tsakanin uku ko fiye da dalilai, a yarda shigarwa ba tare da yin amfani da baka.

Amfani da raba dukiya ba da damar yin wahayinsa Katakon idan akai la'akari da matrix maganganu. Lura, idan muka bude baka, shi wajibi ne don adana da oda daga cikin abubuwan.

Amfani da matrix maganganu ba kawai m rikodin amfani da tsauraran matakan da tsarin na lissafai, amma kuma facilitates aiki da kuma mafita.