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 cov kab ntawm cov matrix koom.
Koj paub li cas yog eigenvectors yog linearly ywj siab?
Eigenvectors sib raug rau cov eigenvalues txawv yog linearly ywj siab. … Yog hais tias muaj dua eigenvalues, tab sis lawv tsis yog (piv txwv li, lawv algebraic multiplicity sib npaug rau lawv cov geometric multiplicity), tib qhov kev ncua sij hawm tuav.
Puas eigenvectors tuaj yeem ua raws li kev vam khom?
Yog A yog N × N complex matrix nrog N txawv eigenvalues, ces txhua txheej N sib raug eigenvectors tsim lub hauv paus rau CN. Pov thawj. Nws yog qhov txaus los ua pov thawj tias cov txheej txheem ntawm eigenvectors yog linearly ywj siab … Txij li txhua Vj=0, ib qho kev cuam tshuam ntawm {Vj} yuav tsum muaj tsawg kawg ob eigenvectors.
Puas yog txhua tus eigenvectors ntawm tib eigenvalue linearly ywj siab?
Eigenvectors sib xws rau cov eigenvalues txawv ib txwm muaj kev ywj pheej. Nws ua raws los ntawm qhov no uas peb tuaj yeem ib txwm diagonalize ib n × n matrix nrog n txawv eigenvalues vim nws yuav muaj n linearly ywj siab eigenvectors.
Thaum eigen qhov tseem ceeb yog linearly ywj siab?
Yog tus eigenvalues ntawm A yog qhov txawv, nws hloov tawm tias eigenvectors yog linearly ywj siab; tab sis, yog tias ib qho ntawm eigenvalues tau rov ua dua, kev tshawb nrhiav ntxiv yuav tsim nyog. qhov twg β thiab γ tsis yog ob leeg sib npaug rau xoom tib lub sijhawm.
