Vim li cas lub hauv paus orthonormal tseem ceeb?

Cov txheej txheem:

Vim li cas lub hauv paus orthonormal tseem ceeb?
Vim li cas lub hauv paus orthonormal tseem ceeb?

Video: Vim li cas lub hauv paus orthonormal tseem ceeb?

Video: Vim li cas lub hauv paus orthonormal tseem ceeb?
Video: Xov Xwm Qhov Tseeb Lub Hauv Paus Kab Mob aw Kis Rau Neeg Vim Li Cas Tham Rau Peb Paub Txog 2024, Kaum ib hlis
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Qhov tshwj xeeb ntawm lub hauv paus orthonormal yog nws ua rau ob qhov sib npaug kawg tuav. Nrog rau lub hauv paus orthonormal, cov kev sib koom tes sawv cev muaj qhov ntev tib yam li cov vectors qub, thiab ua tib lub kaum sab xis nrog ib leeg.

YYuav siv cov orthonormal yog dab tsi?

Cov no yog cov kev hloov pauv uas khaws cia cov khoom sab hauv, thiab hu ua orthogonal transformations. Feem ntau thaum ib tus xav tau lub hauv paus los ua kev suav, nws yooj yim siv lub hauv paus orthonormal. Piv txwv li, cov mis rau ib qhov chaw vector yog qhov yooj yim dua nrog lub hauv paus orthonormal.

Puas orthonormal bases unique?

Tsis yog cov hauv paus tsis muaj qhov tshwj xeeb, muaj ntau yam tsis kawg.

Vim li cas peb thiaj xav tau orthogonal matrix?

Raws li kev hloov pauv hloov pauv, ib qho orthogonal matrix khaws cov khoom sab hauv ntawm vectors, thiab yog li ua raws li isometry ntawm Euclidean qhov chaw, xws li kev sib hloov, kev xav lossis rotoreflection. Hauv lwm lo lus, nws yog kev hloov pauv hloov pauv.

Yuav siv cov vectors orthogonal yog dab tsi?

Txoj Lus Qhia Ib txheej orthogonal ntawm non-zero vectors yog linearly ywj siab. Muab cov txheej txheem ntawm cov vectors ywj siab, feem ntau muaj txiaj ntsig rau hloov lawv mus rau hauv cov txheej txheem orthonormal ntawm vectors. Peb xub txhais tus neeg ua haujlwm projection. Txhais.

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