Cov txheej txheem:
- Puas eigenvalues ntawm AAT thiab ATA tib yam?
- Puas yog ATA tib yam li AAT?
- Puas yog ATA muaj qhov txawv txav?
- Yuav ua li cas sib txawv eigenvectors muaj tib eigenvalue?
Video: Puas aat thiab ata muaj tib eigenvalues?
2024 Tus sau: Fiona Howard | [email protected]. Kawg hloov kho: 2024-01-10 06:38
Yog A yog m × n matrix, ces ATA thiab AAT muaj tib yam nonzero eigenvalues … Yog li ntawd Ax yog ib qho eigenvector ntawm AAT sib raug rau eigenvalue λ. Ib qho kev sib cav sib cav tuaj yeem siv los qhia tias txhua qhov tsis yog xoom eigenvalue ntawm AAT yog eigenvalue ntawm ATA, yog li ua tiav cov pov thawj.
Puas eigenvalues ntawm AAT thiab ATA tib yam?
Cov matrices AAT thiab ATA muaj tib yam nonzero eigenvalues. Tshooj 6.5 tau qhia tias eigenvectors ntawm cov symmetric matrices yog orthogonal.
Puas yog ATA tib yam li AAT?
Vim AAT thiab ATA yog qhov sib luag tiag tiag, lawv tuaj yeem ua rau diagonalized nrog orthogonal matrices. Nws ua raws los ntawm cov nqe lus dhau los (txij li geometric & algebraic multiplicities coincide) uas AAT thiab ATA muaj tib yam eigenvalues.
Puas yog ATA muaj qhov txawv txav?
Nyob. Piv txwv li, yog A= 1 2 3 2 4 −1 3 −1 5 , ces tus cwj pwm sib npaug det(A − λI)=−25 − 15λ + 10λ2 − λ3=0 tsis muaj lub hauv paus rov qab. Li no tag nrho eigenvalues ntawm A yog qhov txawv thiab A yog diagonalizable. 3.35 Rau txhua qhov matrix A, AtA ib txwm diagonalizable.
Yuav ua li cas sib txawv eigenvectors muaj tib eigenvalue?
Ob qhov txawv Eigenvectors sib raug zoo ib yam Eigenvalue ib txwm nyob ntawm. Ob qhov sib txawv Eigenvectors sib haum rau tib Eigenvalue yog ib txwm nyob ntawm linearly.
Pom zoo:
Phyllis thiab michael puas muaj hnub nyoog tib yam?
↑ Hauv lub caij 2, Phyllis hais tias nws tus kheej thiab Michael Scott yog "muaj hnub nyoog tib yam". Michael yug hauv lub Plaub Hlis Ntuj xyoo 1965, txhais tau hais tias Phyllis feem ntau yuav yug hauv xyoo 1965 thiab . Phyllis thiab Michael puas muaj hnub nyoog tib yam?
Eigenvalues thiab eigenfunctions yog dab tsi?
Cov kab zauv zoo li no, qhov twg tus neeg teb xov tooj, ua haujlwm ntawm kev ua haujlwm, tsim lub sijhawm ua haujlwm tas li, hu ua eigenvalue equation. Txoj haujlwm yog hu ua eigenfunction, thiab qhov tshwm sim tus nqi hu ua eigenvalue . txhais li cas los ntawm eigenfunctions thiab eigenvalues?
Puas yog matrix tiag tiag muaj qhov nyuaj eigenvalues?
Vim ib lub matrix tiag tiagmuaj cov eigenvalues complex (tshwm sim nyob rau hauv complex conjugate khub), txawm rau ib tug tiag tiag matrix A, U thiab T nyob rau hauv lub saum toj no theorem yuav complex . Tus nqi tiag tiag puas muaj eigenvectors nyuaj?
Puas muaj kev sib cav uas tsis muaj zog thiab tsis muaj kev ntseeg?
Puas muaj kev sib cav uas tsis muaj zog thiab tsis muaj kev ntseeg? piav qhia: Txhua qhov kev sib cav uas tsis muaj zog kuj yuav tsis muaj kev sib cav, vim tias yuav muaj zog yog ib feem ntawm lub ntsiab lus ntawm kev sib cav . Puas muaj kev sib cav uas tsis muaj zog thiab paub?
Puas yog tib leeg thiab tib leeg xwb?
Raws li nouns qhov txawv ntawm ib leeg thiab solitude yog tias tus kheej yog tus nyob ib leeg, lossis nyob ib leeg; ib tug anchoret, hermit los yog recluse thaum solitude yog ib leeg; lub xeev ntawm nyob ib leeg lossis nyob ib leeg, ntawm tus kheej .
