A matrix yog qhov zoo meej yog tias nws sib luag thiab tag nrho nws cov eigenvalues yog qhov zoo Qhov yog, muaj ntau ntau txoj hauv kev sib npaug los txhais qhov zoo meej matrix meej matrix A matrix yog li no positive-txhais yog thiab tsuas yog tias nws yog lub matrix ntawm daim ntawv zoo-txhais plaub fab lossis Hermitian daim ntawv. Hauv lwm lo lus, matrix yog qhov zoo-txhais tau yog thiab tsuas yog tias nws txhais cov khoom sab hauv. … M yog symmetric los yog Hermitian, thiab tag nrho nws cov eigenvalues yog tiag tiag thiab zoo. https://en.wikipedia.org › wiki › Definite_matrix
Definite matrix - Wikipedia
. Ib qho kev txhais sib npaug tuaj yeem muab tau los siv qhov tseeb tias rau qhov sib luag matrix cov cim ntawm cov pivots yog cov cim ntawm eigenvalues.
txhais li cas yog eigenvalues zoo?
A Hermitian (los yog symmetric) matrixyog qhov tseeb tseeb iff tag nrho nws cov eigenvalues yog qhov zoo. Yog li ntawd, ib tug general complex (feem ntau, tiag) matrix yog zoo meej iff nws Hermitian (los yog symmetric) ib feem muaj tag nrho cov zoo eigenvalues. … Lub matrix inverse ntawm qhov zoo meej matrix kuj yog qhov tseeb.
Yog eigenvalues ib txwm zoo?
yog tias matrix yog qhov zoo (tsis zoo) txhais tau, tag nrho nws cov eigenvalues yog qhov zoo (tsis zoo). Yog hais tias ib tug symmetric matrix muaj tag nrho nws cov eigenvalues zoo (tsis zoo), nws yog qhov zoo (tsis zoo) tseeb.
Puas eigenvalues tsis zoo?
Ib lub matrix ruaj khov yog suav tias yog qhov tseeb thiab qhov zoo. Qhov no txhais tau tias tag nrho cov eigenvalues yuav yog xoom lossis zoo. Yog li ntawd, yog tias peb tau txais qhov tsis zoo eigenvalue, nws txhais tau tias peb qhov tawv nqaij matrix tau ua tsis ruaj khov.
txhais li cas thaum eigenvalues tsis zoo?
Geometrically, ib qho eigenvector, sib raug rau qhov tsis yog zero eigenvalue tiag tiag, cov ntsiab lus nyob rau hauv ib qho kev taw qhia uas nws yog stretched los ntawm kev hloov pauv thiab eigenvalue yog qhov tseem ceeb uas nws ncav cuag. Yog tias qhov eigenvalue tsis zoo, qhov kev taw qhia yog thim rov qab.
