作者armopen (考个没完)
看板Math
标题Re: [线代] similar跟Cayley-Hamilton
时间Wed Aug 17 01:24:45 2011
※ 引述《mqazz1 (无法显示)》之铭言：
: 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
: 请问这两个要怎麽证?
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]
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 114.37.163.98
※ 编辑: armopen 来自: 114.37.163.98 (08/17 01:25)