length of spanning list Nyob rau finnite-dimensional vector space, qhov ntev ntawm txhua daim ntawv teev npe ntawm vectors tsawg dua lossis sib npaug rau qhov ntev ntawm txhua daim ntawv teev cov vectors. Ib qhov chaw vector yog hu ua finnite-dimensional yog qee npe ntawm vectors hauv nws spans qhov chaw.
Koj ua pov thawj li cas qhov chaw vector yog qhov kawg nkaus yog tias nws muaj?
Rau txhua qhov chaw vector muaj lub hauv paus, thiab txhua lub hauv paus ntawm qhov chaw vector muaj qhov sib npaug; Raws li qhov tshwm sim, qhov loj me ntawm qhov chaw vector yog cim tshwj xeeb. Peb hais tias V yog finite-dimensional yog qhov dimension ntawm V yog finite, thiab infinite-dimensional yog nws qhov dimension yog infinite.
Puas yog qhov chaw seem vector qhov kawg?
Txhua lub hauv paus rau qhov chaw seem vector qhov kawg muaj cov lej tib yam. Tus lej no hu ua qhov loj ntawm qhov chaw. Rau cov khoom sab hauv qhov chaw ntawm qhov ntev n, nws tau yooj yim tsim tau tias txhua txheej ntawm n nonzero orthogonal vectors yog lub hauv paus.
Puas tag nrho cov seem vector qhov chaw muaj lub hauv paus?
Summary: Txhua qhov chaw vector muaj qhov basi, uas yog, qhov siab tshaj plaws linearly independent subset. Txhua vector nyob rau hauv ib qhov chaw vector tuaj yeem sau rau hauv ib txoj kev tshwj xeeb raws li kev sib xyaw ua ke ntawm cov ntsiab lus hauv lub hauv paus no.
Puas yog qhov chaw seem vector qhov chaw muaj qhov tsis paub kawg subspace?
INF0: Txhua qhov chaw vector qhov tsis kawg muaj qhov tsis kawgdimensional tsim nyog sub-space. subspace.
