→ maxsho :(e)可對角化不代表他是可逆 如果A有一個eigenvalue=0 08/09 17:43
→ maxsho :則A不可逆 08/09 17:44
→ maxsho :(d) v vector v!=0 f,g different eigenvalues of v 08/09 17:52
→ maxsho :則 fv=Av=gv,so fv-gv=0 but v!=0 so f=g 矛盾 08/09 17:54
[3 4 0 0] [ 3 -4 0 0]
[2 3 0 0] [-2 3 0 0]
[0 0 5 6] 反矩陣 [ 0 0 5 -6]
[0 0 4 5] [ 0 0 -4 5]
請問這個是為什麼?
他是拆成四個方塊矩陣 左下到右上的那條乘-1嗎?
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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
請問這些是為什麼?
謝謝
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