Matrix ngeMathematika. matrix phindo

Okunye Chinese bezibalo yamandulo ezisetyenziswa nemigubasi yabo intelekelelo ngohlobo tabular inani elithile lwemiqolo nemihlathi. Koko, izinto ezifana zezibalo uthatythwa njengo "yembutho magic". Nangona iimeko eyaziwayo ukusetyenziswa amacwecwe ngohlobo zoonxantathu, abangancedekanga zamkelwe ngokubanzi.

Ukuza kuthi ga ngoku, kukho matrix zezibalo ngokuqhelekileyo kakuhle obokt imilo oluxande kwangaphambili inani lwemihlathi kunye nemiqondiso ezichaza imilinganiselo isizalo. Kwimathematika, uhlobo yokurekhoda iye yasetyenziswa ngokubanzi emazishicilelwe ngendlela indawo lweenkqubo zahlula kwakunye kwizibalo yomgama algebra. Kuthathwa ukuba inani lemiqolo kwi matrix lingana ne ukuya kwinani langoku kwinkqubo kwizibalo, inani lwemihlathi ingqamana yimalini engaziwayo kufuneka zichazwe kwi ekuhambeni isisombululo.

Ngaphandle kwento yokuba isizalo ngokwayo apha ekuhambeni isisombululo yayo kukhokelela ekufumaneni semvelo ayaziwa kwindawo nemeko yenkqubo, kukho iqela imisebenzi aljibra ukuba bavunyelwe ukuba uyiweze into elinikiweyo zezibalo. Olu luhlu luquka i kongezwe matrices kokuba nemilinganiselo efanayo. I-phindo ngokwematrisi kunye nemilinganiselo efanelekileyo (kuyenzeka ukuba phinda matrix na elinye icala ukuba inani lwemihlathi lilingane inani lemiqolo ye isizalo kwelinye icala). Kananjalo uvumelekile ukuba phinda matrix yi kumda, okanye elementi okanye isangqa isiseko (ngenye scalar).

Ukuqwalasela lo phindo matrix kufuneka bagadwe ngeliso elibukhali ukuba ngokungqongqo inani lokuqala ntsika lilingane inani lemiqolo le yesibini. Kungenjalo, isenzo isizalo ayichazwanga. Ngokutsho ulawulo, apho i-phindo matrix-matrix, isiqalelo ngasinye uluhlu omtsha kulingana ngexabiso udibaniso iimveliso nelayo imiba imiqolo eziqalelo yokuqala matrix kwezinye iikholam.

Ecacileyo, makhe sihlolisise umzekelo wendlela eyenzeka matrix phindo. Thatha matrix A

February 3 -2

3 4 0

-1 2 -2,

phinda ngayo matrix B

3 -2

1 0

4 -3.

Ilungu kumqolo wokuqala kumhlathi wokuqala isizalo eliphuma ilingana 2 * 3 + 3 * 1 + (- 2) * 4. Ngokunjalo, kumqolo wokuqala kwi element kwikholam yesibini iya kulingana 2 * (- 2) + 3 * 0 + (- 2) * (- 3), njalo-njalo de ngokugcwalisa isiqalelo ngasinye isizalo entsha. Umthetho matrix phindo lubandakanya ukuba umphumo imveliso mxn parameters matrix yi isizalo ukuba nxk ratio, uba itafile ene- ubungakanani m x k. Emva lo mthetho, siyakwazi ukubona ukuba imveliso matrices ekuthiwa-isikwere, ngokulandelelana, i-odolo elinye lisoloko ichaziwe.

Ukususela iipropati ubephethwe matrix phindo kufuneka yabelwe ngokungathi iyinyaniso esisiseko ukuba lo msebenzi ayikho Ihlelo. Yiloo nto ke imveliso ye matrix M N akalingani imveliso N ngu M. Ukuba matrices isikweri umyalelo inye waphawula ukuba imveliso zabo phambili kwaye reverse usoloko uzimisele, ezahlukeneyo kuphela isiphumo, isizalo eziziingxande ngathi iimeko ezithile azisoloko sizaliseke.

E matrix phindo kukho iqela kwiipropati abe bubungqina ecacileyo zezibalo. Associativity Ekwandeni kuthetha inkcaneko ilandelayo Ukuzibonakalisa ngokwezibalo: (MN) K = M (NK), apho M, N, kwaye K - matrix ukuba imida apho phindo ichazwa. Distributivity phindo luthatha ukuba M (N + K) = MN + MK, (M + N) K = MK + NK, L (MN) = (LM) N + M (LN), apho L - inani.

Iziphumo iimpawu phindo matrix, ebizwa i "ukudibanisa", kulandela ukuba kwimveliso equlathe phakathi izinto ezintathu okanye ngaphezulu, ukuba ukungena ngaphandle kokusebenzisa kwizibiyeli.

Ukusebenzisa ipropati nosasazwayo unika ithuba lokuba kuvele braces xa kuqwalaselwa amabinzana matrix. Nceda uqaphele, ukuba sivula kwizibiyeli, kuyimfuneko ukuba kulondolozwe ngokomyalelo imiba.

Ukusebenzisa amabinzana matrix na irekhodi compact iinkqubo kuphela ngumsina kwizibalo, kodwa kube lula inkqubo kunye nezisombululo.