-matrix Mathematical. matrix

Okuningi wezibalo lasendulo Chinese elisetshenziswa kokuthunyelwe kwabo ikhompyutha in ifomu tabular enenani elithile lemigqa namakholomu. Khona-ke, sengathi wetintfo tetibalo ukubizwa ngokuthi "square eliwumlingo". Nakuba izimo aziwayo ukusetshenziswa amathebula e ngesimo onxantathu, futhi azikaze kabanzi yokutholwa.

Kuze kube manje, matrix zezibalo elivame ukuqondwa obokt ukuma unxande nge predetermined shicilelo amakholomu kanye nezimpawu ukuthi ichaze izilinganiso matrix. Esifundweni sezibalo, uhlobo sokurekhoda kabanzi ngokurekhoda ifomu compact umehluko izinhlelo kanye lwento zibalo Aljibhra. Kusolwa ukuthi inani lemigqa ku-matrix elilingana inombolo ekhona ohlelweni of zibalo, inani amakholomu oluhambisana kangakanani akwaziwa kumele kuchazwe ngokuhamba ikhambi.

Ngaphandle kweqiniso lokuthi kwabathile matrix ngokwayo ngokuhamba isixazululo yayo kuholela ekutholeni esingokwemvelo okungaziwa isimo kohlelo, zikhona eziningi imisebenzi algebraic ukuthi bavunyelwe ngesikhathi esinikeziwe into zezibalo. Lolu hlu lufaka phakati kwalokho-matrices kokuba izilinganiso zobukhulu efanayo. Ukuphindwaphindwa matrices nge Ubukhulu ezifanele (kungenzeka ukuba azale ande matrix nge uhlangothi kokuba eziningi amakholomu ilingana inombolo yemigqa we matrix ngakolunye uhlangothi). Futhi akuvumelekile ukuba azale ande matrix ngumuntu vector, noma i-elementi noma base indandatho (ngenye scalar).

Uma ucabangela ukubuyabuyelela-matrix kumelwe ziqashwe ukuze ngokuqinile inombolo yokuqala amakholomu ilingana inombolo yemigqa lesibili. Kungenjalo, isenzo we matrix akachaziwe. Ngokusho umthetho, lapho ukubuyabuyelela-matrix-matrix, element ngayinye ku array entsha okulingana isamba imikhiqizo esihambelanayo tincenye imigqa izici matrix yokuqala kusuka kwamanye amakholomu.

Ngokucaca, ake sicabangele isibonelo sendlela matrix kwenzeka. Thatha matrix A

Februwari 3 -2

3 4 0

-1 2 -2,

kuphinde by matrix B

3 -2

1 0

4 -3.

I element of emgqeni wokuqala kukholomu yokuqala matrix okuholela ilingana 2 * 3 + 3 * 1 + (- 2) * 4. Ngakho, emgqeni wokuqala e yesibili kukholomu isici ngeke zilingane 2 * (- 2) + 3 * 0 + (- 2) * (- 3), nokunye kuze ukugcwalisa element we matrix omusha ngamunye. Rule matrix kuhilela ukuthi umphumela umkhiqizo MXN-matrix imingcele ngu matrix kokuba nxk isilinganiso, iba itafula elinendawo Usayizi m x k. Ukulandela lesi simiso, singaphetha ngokuthi umkhiqizo okuthiwa matrices sikwele, ngokulandelana, we-oda efanayo njalo echaziwe.

Kusukela izakhiwo emimoya matrix kufanele zabelwe njengoba iqiniso eliyisisekelo ukuthi lo msebenzi akuyona commutative. Lowo umkhiqizo we-matrix M ukuze N akulingani umkhiqizo N by M. Uma e matrices skwele oda efanayo waphawula ukuthi umkhiqizo wabo phambili futhi reverse njalo kunqunywa, ezingafani kuphela yalokho, matrix unxande efana izimo ezithile awagcwaliseki njalo.

Ngo matrix zikhona eziningi izindawo ukuthi abe nga cwatha bonakaliso zezibalo. Associativity ukwandiswa kusho zibonise ukwethembeka elandelayo isibalo sezibalo: (MN) K = M (NK), lapho M, N, kanye K - matrix kokuba nemingcele lapho ukubuyabuyelela kuchazwa. Distributivity ukubuyabuyelela izitshela ukuthi M (N + K) = MN + MK, (M + N) K = MK + NK, L (MN) = (LM) N + M (LN), lapho L - inombolo.

Umphumela we izakhiwo ukuphindwaphindwa-matrix, ebizwa ngokuthi "associative", kusobala ukuthi umkhiqizo aqukethe phakathi izici ezintathu noma ngaphezulu, ukungena ngaphandle kokusebenzisa kubakaki kuvumelekile.

Ukusebenzisa impahla wokusakaza kunikeza ithuba lokuba kuvele ukuthi besokunxele lapho ucabangela izinkulumo-matrix. Sicela uqaphele, uma sivula kubakaki, kubalulekile ukuba alondoloze oda zezici.

Ukusebenzisa inkulumo ethi-matrix hhayi kuphela irekhodi compact izinhlelo nzima of zibalo, kodwa futhi kusiza ukucubungula kanye nezixazululo.