Definition. Ib qho tsis muaj npe ntawm cov vectors tsis yog xoom hauv R yog hu ua orthogonal teeb yog tias txhua khub ntawm cov vectors sib txawv hauv cov teeb yog orthogonal. Orthogonal poob lawm yog cia li linearly ywj siab. Theorem Ib txheej orthogonal ntawm vectors yog linearly ywj siab.
Puas yog txhua txoj kev ywj pheej teeb tsa ib qho orthogonal?
Tsis yog txhua qhov kev ywj pheej teeb tsa hauv Rn yog qhov teeb tsa orthogonal. … Yog hais tias y yog linear ua ke ntawm nonzero vectors los ntawm ib qho orthogonal teeb, ces cov luj nyob rau hauv lub linear ua ke yuav raug xam tsis muaj kab khiav hauj lwm ntawm ib tug matrix.
Is linearly ywj siab orthogonal?
Txoj lus Ib qho orthogonal txheej ntawm cov vectors tsis yog xoom yog linearly ywj siab. Muab cov txheej txheem ntawm cov vectors ywj pheej, nws feem ntau muaj txiaj ntsig los hloov lawv mus rau hauv cov txheej txheem orthonormal ntawm vectors.
Qhov txawv ntawm orthogonal thiab linearly ywj siab yog dab tsi?
Cov lus teb thiab cov lus teb
Raws li kuv nkag siab, cov txheej txheem ntawm cov vectors ywj pheej txhais tau tias nws tsis tuaj yeem sau ib qho ntawm lawv raws li lwm tus. ib txheej ntawm orthogonal vectors txhais tau tias cov khoom lag luam ntawm ob ntawm lawv yog xoom.
Do linearly ywj vectors ib txwm span?
Kev ncua ntawm ib txheej vectors yog cov txheej txheem ntawm txhua qhov kev sib txuas ntawm cov vectors. … Yog tias muaj cov kev daws teeb meem uas tsis yog xoom, ces cov vectors yog linearly dependent. Yog tustsuas yog x=0, ces lawv yog linearly ywj siab. Lub hauv paus rau subspace S ntawm Rn yog ib txheej ntawm vectors uas spans S thiab yog linearly ywj siab.
