Theorem: Rau ib square matrix ntawm kev txiav txim n, cov hauv qab no yog sib npaug: A yog invertible. Nullity ntawm A yog 0. … Lub system Ax=0 tsuas muaj qhov kev daws teeb meem tsis tseem ceeb.
Dab tsi yog qhov tsawg kawg ntawm nullity ntawm matrix?
Siv qhov tseeb tias qib siab tshaj plaws yog min{m, n}, peb tuaj yeem txiav txim siab tias qhov tsawg kawg nkaus nullity yog n−min{m, n}=n+max{−m, − n}=max{n−m, 0}. Hauv lwm lo lus, yog n≤m, ces qhov tsawg kawg nkaus nullity yog 0, txwv tsis pub yog n>m, ces qhov tsawg kawg nkaus nullity yog n-m.
Puas yog qhov loj me ntawm qhov chaw tsis muaj 0?
Yog, dim(Nul(A)) yog 0. Nws txhais tau tias tus nullspace tsuas yog xoom vector. Qhov chaw null yuav ib txwm muaj xoom vectors, tab sis tuaj yeem muaj lwm cov vectors zoo li.
Puas yog qhov chaw tsis muaj qhov khoob?
Vim T ua rau ntawm qhov chaw vector V, ces V yuav tsum suav nrog 0, thiab txij li peb pom tias nullspace yog subspace, ces 0 yeej ib txwm nyob rau hauv nullspace ntawm daim ntawv qhia kab, yog li ntawd nullspace ntawm daim ntawv qhia kab tsis tuaj yeem tsis muaj qhov khoobvim nws yuav tsum muaj tsawg kawg ib lub ntsiab lus, xws li 0.
Puas muaj peev xwm rau matrix kom muaj qib ntawm 0?
Yog li yog tias lub matrix tsis muaj cov khoom nkag (piv txwv li qhov xoom matrix) nws tsis muaj linearly lindependant kab lossis kab, thiab yog li muaj qib xoom. Yog hais tias lub matrix muaj tsuas yog 1 nkag, ces peb muaj ib tug linearly ywj siab kab thiab kab, thiab cov qeb yog li 1, yog li nyob rau hauv xaus, tsuas yog qeb 0 matrix yog xoom matrix
