作者mqazz1 (无法显示)
看板Math
标题[线代] 反矩阵和一些对角化观念
时间Tue Aug 9 14:40:22 2011
[3 4 0 0] [ 3 -4 0 0]
[2 3 0 0] [-2 3 0 0]
[0 0 5 6] 反矩阵 [ 0 0 5 -6]
[0 0 4 5] [ 0 0 -4 5]
请问这个是为什麽?
他是拆成四个方块矩阵 左下到右上的那条乘-1吗?
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(c) If A is diagonalizable, then the columns of A are linearly independent
False
(d) A nonzero vector cannot correspond to two different eigenvalues of A
True
(e) A matrix A is invertible if and onlu if there is a coordinate system
in which the transformation x |-> Ax is repressented by a diagonal matrix
False
请问这些是为什麽?
谢谢
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1F：→ maxsho :(e)可对角化不代表他是可逆 如果A有一个eigenvalue=0 08/09 17:43
2F：→ maxsho :则A不可逆 08/09 17:44
3F：→ maxsho :(d) v vector v!=0 f,g different eigenvalues of v 08/09 17:52
4F：→ maxsho :则 fv=Av=gv,so fv-gv=0 but v!=0 so f=g 矛盾 08/09 17:54