Kulolu shicilelo, sizocubungula incazelo nezinto eziyinhloko ze-matrix ngezibonelo, ububanzi bayo, futhi sinikeze nesizinda esifushane somlando mayelana nokuthuthukiswa kwethiyori ye-matrix.
Incazelo ye-Matrix
Matrix iwuhlobo lwethebula elingunxande eliqukethe imigqa namakholomu aqukethe izakhi ezithile.
Usayizi we-matrix usetha inani lemigqa namakholomu, akhonjiswa ngezinhlamvu m и n, ngokulandelana. Ithebula ngokwalo lakhiwe ngabakaki abayindilinga (kwesinye isikhathi abakaki abayisikwele) noma imigqa eqondile eyodwa/emibili eqondile.
I-matrix iboniswa ngohlamvu olukhulu A, kanye nenkomba yobukhulu bayo - Amn. Isibonelo siboniswa ngezansi:
Ukusetshenziswa kukamatikuletsheni kuzibalo
Ama-matrices asetshenziselwa ukubhala nokuxazulula noma amasistimu wezibalo ezihlukene.
Izakhi ze-matrix
Ukukhombisa izakhi ze-matrix, kusetshenziswe notation ejwayelekile aij, lapho:
- i – inombolo yomugqa oqukethe isici esinikeziwe;
- j – ngokulandelana, inombolo yekholomu.
Isibonelo, ku-matrix engenhla:
- a24 = 1 (umugqa wesibili, ikholomu yesine);
- a32 = 16 (umugqa wesithathu, ikholomu yesibili).
Imigqa
Uma zonke izici zomugqa we-matrix zilingana noziro, umugqa onjalo ubizwa null (kugqanyiswe ngokuluhlaza).
Uma kungenjalo, umugqa uwukuthi nonzero (kugqanyiswe ngokubomvu).
Ama-diagonals
I-diagonal edwetshwa kusukela ekhoneni elingenhla kwesokunxele le-matrix kuya kwesokudla esingezansi kubizwa eziphambili.
Uma i-diagonal idwetshwa kusukela phansi kwesokunxele kuya phezulu kwesokudla, ibizwa ngokuthi ukubambisana.
Imininingwane yomlando
"I-Magic Square" - ngaphansi kwaleli gama, ama-matrices akhulunywe okokuqala e-China yasendulo, futhi kamuva phakathi kwezibalo zama-Arab.
Ngo-1751 isazi sezibalo saseSwitzerland uGabriel Cramer sanyathelisa "Umthetho kaKramer"esetshenziselwa ukuxazulula amasistimu ezibalo ze-algebraic linear (SLAE). Cishe ngesikhathi esifanayo, "indlela ye-Gauss" yavela ukuze kuxazululwe i-SLAE ngokususa okulandelanayo kokuguquguqukayo (umbhali nguCarl Friedrich Gauss).
Igalelo elibalulekile ekuthuthukisweni kwethiyori ye-matrix nalo lenziwa izazi zezibalo ezinjengoWilliam Hamilton, u-Arthur Cayley, uKarl Weierstrass, uFerdinand Frobenius noMarie Enmond Camille Jordan. Igama elifanayo elithi "matrix" ngo-1850 lethulwa nguJames Sylvester.