Puas yog matrix zoo ib yam li nws qhov kev hloov pauv?
Puas yog matrix zoo ib yam li nws qhov kev hloov pauv?

Video: Puas yog matrix zoo ib yam li nws qhov kev hloov pauv?

Video: Puas yog matrix zoo ib yam li nws qhov kev hloov pauv?
Video: qhia poj niam txoj kev zoo nyob thaum nrog txiv neej pw saum txaj 2024, Kaum ib hlis
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Cia li xav txog 2 x 2 matrix uas yog zoo ib yam li nws inverse tsis muaj kab pheeb ces kaum nkag yog 1 lossis -1. Diagonal matrices yuav ua. Yog li, A thiab thim rov qab ntawm A yog zoo sib xws , yog li lawv eigenvalues yog tib yam. Yog tias ib qho ntawm A's eigenvalues yog n, eigenvalues ntawm nws inverse yuav yog 1/n.

Kuj nug, puas yog matrix zoo ib yam li nws transpose?

Txhua square matrix tshaj ib daim teb yog zoo ib yam li nws transpose thiab txhua qhov square complex matrix yog zoo sib xws mus rau ib tug symmetrical complex matrix.

Ib yam li ntawd, tag nrho cov invertible matrices zoo sib xws? Yog A thiab B yog zoo sib xws thiab invertible , ces A-1 thiab B-1 yog zoo sib xws . Pov thawj. Txij li thaum tag nrho tus matrices yog invertible , peb tuaj yeem coj qhov hloov pauv ntawm ob sab: B–1 = (P–1AP)–1 = P–1A–1(P–1)–1 = P–1A–1P, yog li A–1 thiab B–1 yog zoo sib xws . Yog A thiab B yog zoo sib xws , yog li Ak thiab Bk rau ib qho k = 1, 2,.

Hais txog qhov no, lub matrix puas zoo ib yam li nws tus kheej?

Ntawd yog, Ib matrix yog zoo ib yam li nws tus kheej : I-1AI = A. Yog A yog zoo sib xws rau B, ces B yog zoo sib xws to A: yog B=P−1AP, ces A=PBP−1=(P−1)−1BP−1. Yog A yog zoo sib xws rau B ntawm B = P−1AP, thiab C yog zoo sib xws rau B ntawm C = Q−1BQ, ces A yog zoo sib xws rau C: C=Q−1P−1APQ=(PQ)−1APQ.

Nws txhais li cas yog matrices zoo sib xws?

Hauv linear algebra, ob n-by-n matrices A thiab B hu ua zoo ib yam li yog muaj ib tug invertible n-by-n matrix P zoo li ntawd. Zoo sib xws matrices sawv cev rau tib daim ntawv qhia kab hauv qab ob (tejzaum) sib txawv hauv paus, nrog P yog qhov hloov ntawm lub hauv paus matrix.

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