Feem ntau, rau ib qho matrix, the eigenvectors tsis yog ib txwm orthogonal. Tab sis rau ib hom tshwj xeeb ntawm matrix, symmetric matrix, eigenvalues yeej ib txwm muaj tseeb thiab cov eigenvectors sib raug zoo ib txwm orthogonal.
Puas yog eigenvectors ntawm eigenvalues ib txwm orthogonal?
Tsis tas txhua qhov orthogonal. Txawm li cas los xij ob eigenvectors sib haum rau cov eigenvalues sib txawv yog orthogonal. Piv txwv li Cia X1 thiab X2 yog ob lub eigenvectors ntawm matrix A sib raug rau eigenvalues λ1 thiab λ2 qhov twg λ1≠λ2.
Puas tag nrho cov symmetric matrices muaj orthogonal eigenvectors?
Yog tias tag nrho cov eigenvalues ntawm symmetric matrix A yog qhov txawv, lub matrix X, uas muaj raws li nws cov kab sib txuas eigenvectors, muaj cov cuab yeej uas X X=I, i.e. X yog ib qho orthogonal matrix.
Puas yog cov matrix tsis sib xws puas muaj orthogonal eigenvectors?
As opposed to the symmetric problem, the eigenvalues a of non-symmetric matrix do not form an orthogonal system. … Thaum kawg, qhov kev sib txawv thib peb yog qhov eigenvalues ntawm cov matrix uas tsis yog-symmetric yuav nyuaj (raws li yog lawv cov eigenvectors sib thooj).
Yog eigenvectors linearly ywj siab?
Eigenvectors sib haum rau cov eigenvalues txawv yog linearly ywj siab. Raws li qhov tshwm sim, yog tias tag nrho cov eigenvalues ntawm lub matrix yog qhov txawv, ces lawv cov eigenvectors sib raug zoo hla qhov chaw ntawm kab vectors uas covkab ntawm matrix belongs.
