Matrix Xisaabeed. dhufashada furta

More xisaabta Chinese qadiimiga ah loo isticmaalo in post xisaabinta ay qaab tabular la tiro gaar ah oo saf oo tiirar. Markaas, sida walxaha xisaabeed gudbiyo sida "square sixir". In kasta oo kiis la yaqaan oo ah isticmaalka loox qaab saddexagal, taas oo aan la ballaaran loo qaatay.

Si aad u taariikhda, shax xisaabeed caadi fahamsan yahay qaab obokt qaab tiro Fundka of columns iyo calaamadaha in la qeexo dhinacyada of furta. In xisaabta, nooc ka mid ah wax lagu qoro ayaa si ballaaran loo isticmaalo diiwaan foom is haysta ee hababka kala duwan iyo sidoo kale ee isleegyada aljabra toosan. Waxaa la malaysan in tirada saf ee maxalka furta oo loo siman yahay inuu joogo tirada nidaamka isleegyo ah, tirada tiirar u dhiganta sida badan aan la aqoon waa in la qeexaa in koorsada ee xalka.

Ka sokow xaqiiqda ah in furta oo iniinahoodu ku dhex jiraan dabcan ay xal u keenaysaa in loo helo oo aan la garaneyn soo jireenka ah ee xaaladda nidaamka, waxaa jira tiro ka mid ah hawlaha aljabrada in la ogol yahay in ay qaadaan in ka badan wax la siiyo xisaabta. Liiska waxaa ka mid ah dheer ee matrices isagoo la cabbir ah. dhufashada ee matrices la cabbir ku haboon (waxaa suurto gal ah in lagu dhufto shax la hal dhinac isagoo tiro ka mid ah tiirar loo siman yahay tirada saf oo furta oo dhinaca kale). Waxaa sidoo kale loo ogol yahay in lagu dhufto shax by dulinka ah, ama element ama giraanta salka (haddii kale scalar).

Fiirsaneysa inay isku dhufashada furta oo waa in la si dhow ula socdo si adag lambarka koowaad ee columns loo siman yahay tirada saf oo labaad. Haddii kale, tallaabada ee maxalka furta oo aan la qeexay. Sida laga soo xigtay xeerka, by kaas oo isku dhufashada furta-furta, element kasta diyaariyeen cusub u dhiganta wadarta soo saarka ee u dhiganta xubno ka mid ah saf oo ka mid ah xubno ka furta ugu horeysay ka columns kale.

Waayo, Hufnaan, ha ka fikiro si aynu tusaale u ah sida isku dhufashada furta dhacdaa. Qaado furta A

February 3 -2

3 4 0

-1 2 -2,

badin by shaxda B ee

3 -2

1 0

4 -3.

element ee safka kowaad ee tiirka koowaad ee maxalka furta oo keentay le'eg yahay ilaa 2 * 3 + 3 * 1 + (- 2) * 4. Iyadoo la raacayo, ee safka kowaad ee element safka labaad barbareyn doonaa 2 * (- 2) + 3 * 0 + (- 2) * (- 3), iyo wixii la mid ah ilaa iyo buuxinta ee element kasta oo furta oo cusub. dhufashada Rule furta oo ku lug leh in natiijada mxn saarka xuduudaheedu furta by furta isagoo nxk cabirku yahay, ayaa noqonaya miis taas oo uu leeyahay a size of m k x. Ka dib markii qaanuunkan, waxaannu ku tirinnaa karaa in wax soo saarka ee waxa loogu yeero matrices square, siday u kala horreeyaan, ee si la mid ah waxaa had iyo jeer lagu qeexay.

Laga soo bilaabo guryaha hantiyeen by dhufashada furta waa in loo qoondeeyay sida xaqiiqda aasaasiga ah in howlgalkan ma aha hormagalinta. Taasi waa wax soo saarka ee M furta in N ma qummana in wax soo saarka ee N by M. Haddii in matrices square ah si la mid ah ayaa lagu arkay in horay iyo dambe ay wax soo saarka waxa markasta ka go'an, kala duwan oo kaliya in natiijada, furta oo qaab sida shuruudo gaar ah oo aan la had iyo jeer waa rumoobay.

In shaxda isku dhufashada waxaa jira tiro ka mid ah guryaha in ay leeyihiin a xujooyin xisaabeed cad. tarmo Associativity macnaheedu waa inay aaminnimo socda hadal xisaabta: (MN) K = M (NK), halkaas oo M, N, iyo K - shax isagoo koobin ee oo isku dhufashada waxaa lagu qeexaa. dhufashada Distributivity muuqataa in M (N + K) = MN + MK, (M + N) K = MK + NK, L (MN) = (su'aaalo) N + M (lihida), halkaas oo L - tirada.

cidhibtii oo ka mid ah sifooyinka isu-dhufasho furta, loo yaqaan "israacinayo", waxaa soo socota in wax soo saarka oo ay ku jiraan inta u dhaxaysa saddex ama in ka badan qodobada, oggol yahay entry aan isticmaalka ku dhxe.

Isticmaalka hantida furfurista siinayaa fursad ay ku muujin biraha markii la tixgelinayo tibaaxaha furta. Fadlan ogsoonow, haddii aan qaansada ku furo, waxaa lagama maarmaan ah si loo ilaaliyo si ay arrimaha.

Isticmaalka tibaaxaha furta oo aan record is haysta nidaamka eheeyn kaliya isleegyo, laakiin sidoo kale fududeeyaa ee processing iyo xal.