Re: [線代] R(A)和N(A^T)

[tibicos (tibicos)]

※ 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)

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 111.252.9.218
推 mqazz1      :謝謝!!