The ehupfumi of chizvaro yayo determinant

Properties pamusoro matrices - mubvunzo kuti vakawanda zvingakonzera dambudziko. Naizvozvo zvakafanira kufunga zvizere.

Matrix - a rectangular tafura mufananidzo, kusanganisira nhamba uye zvinhu. Uyewo, zviri yakatarwa nhamba mhando iyi uye ne zvimwe mamiriro iyo yakanyorwa somunhu rectangular tafura zvinosanganisira imwe nhamba mitsara neshongwe. tafura iyi inofanira akanyudzwa muzvikomberedzo. Zvinogona kuva kumativi mumabhuraketi, muzvikomberedzo, mativi mhando kana yakananga-mhando mumabhuraketi maviri. Vose zviverengo chizvaro vakadamwa - chizvaro maatomu akafanana, uye vane Coordonatele zvavo vari patafura mumunda. Matrix compulsorily akasarudzwa netsamba guta rechiLatin arufabheti.

Properties pamusoro matrices kana kwemasvomhu matafura dzinosanganisira zvinhu. Kuwedzera uye kubvisa pamusoro matrices chinhu nokuda maatomu akafanana kunosvika zvachose. Chokuwanziridza uye weboka kunze kuri kuitwa zvavo svomhu. Kuwanda imwe chizvaro mumwe, zvinokosha kuyeuka mashoko pamusoro scalar zvinobikwa Vector kune mumwe.

C = (a, b) = 1 b 1 + 2 b 2 + ... + mumwe N b N

Properties kuti chizvaro chokuwanziridza mamwe nuances. Zvinobikwa mumwe chizvaro kune umwe dzisiri commutative, kureva, (a, b) asingatadzi kuenzana (a, b).

The inokosha ehupfumi pamusoro matrices zvinosanganisira chinhu chakadai chiyero undere. Chiyero tsika kuti matafura akadaro anonzi kuti determinant. Determinant - mumwe kushanda anoverengeka zvemamiriro sikweya chizvaro pakati hurongwa n. Nemamwe mashoko, determinant anonzi determinants. A tafura yechipiri-kuitira musiyano akaenzana determinant chezvinhu zviri nhamba kana zvinhu zviri diagonals maviri chizvaro A11A22-A12A21. The determinant of chizvaro kuti yepamusoro hurongwa determinants akaratidza zvinogumbura ayo.

Kuti tinzwisise kuti chizvaro vakaderera, pfungwa yakadaro wakatangwa somunhu chinzvimbo (chinzvimbo) pakati chizvaro. Grade - uwandu linearly akazvimirira mbiru uye mitsara tafura. Chizvaro inogona inverted chete kana zvizere chinzvimbo, i.e. chinzvimbo (A) akaenzana N.

Properties pamusoro determinants ose matrices dzinosanganisira:

1. Nokuti determinant ane mativi chizvaro haachinji panguva yayo transposition. Ndizvo determinant pakati chizvaro zvichava akaenzana determinant iri tafura transposed muchimiro.

2. Kana mbiru, kana tambo kuchasanganisira chete zeros, ipapo determinant munhu chizvaro akadaro achava akaenzana razero.

3, chiratidzo determinant ane tafura akadaro richachinja kuti pakatarisana Kana chizvaro chero mbiru mbiri kana chero misara miviri interchanged.

4. Kana mbiru kana musara chizvaro zvikawanda upi nhamba, ipapo ayo determinant zvikawanda maererano chete nhamba.

5. Kana chinhu chizvaro zvakanyorwa sezvo Verengai maviri kana kupfuura zvinoriumba, asi determinant patafura iyi zvakanyorwa sezvo mubatanidzwa determinants anoverengeka. Mumwe determinant kuti mari iyi - ndiwo determinant pakati chizvaro, iyo panzvimbo chinhu anomiririrwa pachiyero, yakanyorwa mumwe mashoko yaizvozvo, ukuwo nharungano determinant.

6. Kana chizvaro pane misara miviri akafanana zvinhu kana maviri chete mbiru, iyo determinant patafura iyi yakaenzana razero.

7. Uyewo, determinant akaenzana razero ari chizvaro yakadaro, umo mbiru mbiri kana mitsara vari Proportional kune mumwe.

8. Kana zvinhu mwanda kana mbiru kane chero nhamba uye zvino wedzera kwavari vamwe zvinhu mumutsetse kana shongwe chete chizvaro, ukuwo, ipapo determinant patafura iyi hakuzochinji.

In yose, tinogona kutaura kuti zvivako zviri chizvaro ari kutaridza kunzwisisa, asi panguva imwe chete anodiwa ruzivo pamusoro pezvakaita kwemasvomhu dzakabatana. Vose ehupfumi ose chizvaro anoenderana yenhengo dzayo uye zvinhu.