随笔分类 -  Matrix Analysis

摘要:We consider $det(A\otimes B)$. Notice that $det(A\otimes B)=det(A\otimes II\otimes B)=det(A\otimes I)det(I\otimes B)$. Hence we have $det(A\otimes B)= 阅读全文
posted @ 2022-10-12 16:27 narip 阅读(93) 评论(0) 推荐(0)
摘要:Proposition (The orthogonal complement of a column space). Let A be a matrix and let $W=\operatorname{Col}(A)$. Then $$ W^{\perp}=\operatorname{Nul}\l 阅读全文
posted @ 2022-10-01 14:07 narip 阅读(31) 评论(0) 推荐(0)
摘要:Norm Norm for vectors \[ \begin{aligned} &\|x\| \geq 0 \\ &\|x\|=0 \text { if and only if } x=0 \\ &\|c x\|=|c|\|x\| \\ &\|x+y\| \leq\|x\|+\|y\| \end{ 阅读全文
posted @ 2022-02-24 21:48 narip 阅读(42) 评论(0) 推荐(0)