作者tibicos (tibicos)
看板Math
標題Re: [線代] R(A)和N(A^T)
時間Mon Jun 6 21:46:56 2011
※ 引述《mqazz1 (無法顯示)》之銘言：
: let A be an m*n matrix
: show that if x 屬於 N(A^T * A), then Ax is in both R(A) and N(A^T)
: 請問這題應該怎麼證呢?
: 請各位指點一下 謝謝!!
(1) Given x is n-by-1. Ax is in R(A) (by definition)
(2) x is in N(A^T*A) -> A^T*Ax=0 <-> A^T(Ax)=0 <-> Ax is in N(A^T)
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1F：推 mqazz1 :謝謝!! 06/07 00:02