※ 引述《mqazz1 (無法顯示)》之銘言：
: A invertible matrix can be similar to a singular matrix
: False
Let A be an invertible matrix which is similar to a singular matrix B.
Then there is an invertible matrix P so that P^{-1} A P = B.
Taking determinant on both sides, we have det(A) = det(B) since
for two square n by n matrices D, E, det(DE) = det(D)det(E).
This is impossible since det(A) is nonzero and det(B) = 0.
: A symmetric matrix can be similar to a nonsymmetric matrix
: True
: 請問這兩個要怎麼證?
We give an example as follows:
Take A = [1 2] and P = [1 1]. Then P A P^{-1) = [-3 3] is not symmetric.
[2 -2] [1 2] [ 9 7]
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※ 編輯: armopen 來自: 114.37.163.98 (08/17 01:25)