Ib qho eigenvalue yog tus lej, qhia koj ntau npaum li cas qhov sib txawv ntawm cov ntaub ntawv nyob rau hauv qhov kev taw qhia, hauv qhov piv txwv saum toj no eigenvalue yog tus lej qhia peb li cas nthuav tawm cov cov ntaub ntawv yog nyob ntawm kab. … Qhov tseeb tus nqi ntawm eigenvectors/values uas muaj nyob sib npaug li tus naj npawb ntawm qhov ntev ntawm cov ntaub ntawv teev muaj.
Tus nqi eigen txhais li cas?
Qhov sib thooj eigenvalue, feem ntau denoted los ntawm., yog qhov xwm txheej uas tus eigenvector yog ntsuas. Geometrically, ib qho eigenvector, sib raug rau qhov tsis yog xoom eigenvalue, cov ntsiab lus nyob rau hauv ib qho kev taw qhia uas nws yog ncab los ntawm kev hloov pauv thiab eigenvalue yog qhov tseem ceeb los ntawm qhov uas nws ncav cuag.
eigenvectors qhia dab tsi?
Vim cov Eigenvectors qhia kev taw qhia ntawm lub ntsiab lus tseem ceeb (txoj haujlwm tshiab), peb yuav muab cov ntaub ntawv qub los ntawm eigenvectors kom rov taw qhia peb cov ntaub ntawv mus rau lub axes tshiab. Cov ntaub ntawv rov taw qhia no yog hu ua tus qhab nia.
Vim li cas peb thiaj xav tau eigenvalues?
Tshuaj teb. Eigenvectors ua kom nkag siab txog kev hloov pauv yooj yim. Lawv yog cov "axes" (kev taw qhia) raws li ib tug linear transformation ua tsuas yog los ntawm "stretching / compressing" thiab / los yog "flipping"; eigenvalues muab rau koj los ntawm qhov kev sib koom ua ke no tshwm sim.
eigenvalue ntawm 0 txhais li cas?
Yog tias 0 yog eigenvalue, ces tus nullspace tsis tseem ceeb thiab matrix yogtsis invertible.
