x*****d
发帖数: 427 | 1 发信人: cheeryyu (浪人清歌), 信区: Mathematics
标 题: [转载] How to calculate det(A)???
发信站: The unknown SPACE (Thu May 29 20:53:48 2003), WWW转贴
【 以下文字转载自 EE 讨论区,原文如下 】
发信人: cheeryyu (浪人清歌), 信区: EE
标 题: How to calculate det(A)???
发信站: The unknown SPACE (Thu May 29 20:26:04 2003) WWW-POST
A is a Hermitian matrix with complex values, all the diagonal values equals to
1, and the norm of all the off-diagonal values are less than 1.
Now I guess det(A) <= 1? that is, the product of all the eigenvalues are less | l*******s
发帖数: 7316 | 2 如果A是对角占优的话，det(A)可能小于1。
如果A是实对称对角占优阵，A就是实对称正定阵。eig(A)>0
这也许可以推广到Hermitian matrix with complex values。
另外给一个求下面类型矩阵所有特征值的技巧
d a a ... a
a d a ... a
A= ...............
a a a ... a
a a a ... d
a,d are real, A is nXn matrix.
let B=A-(d-a)I, then
a a a ... a
a a a ... a
B= ...............
a a a ... a
a a a ... a
eig(B)={0,0,...0,na}
eig(A)={d-a,d-a,...d-a,d+na-a}
to
less
【在 x*****d 的大作中提到】
: 发信人: cheeryyu (浪人清歌), 信区: Mathematics
: 标 题: [转载] How to calculate det(A)???
: 发信站: The unknown SPACE (Thu May 29 20:53:48 2003), WWW转贴
: 【 以下文字转载自 EE 讨论区,原文如下 】
: 发信人: cheeryyu (浪人清歌), 信区: EE
: 标 题: How to calculate det(A)???
: 发信站: The unknown SPACE (Thu May 29 20:26:04 2003) WWW-POST
: A is a Hermitian matrix with complex values, all the diagonal values equals to
: 1, and the norm of all the off-diagonal values are less than 1.
: Now I guess det(A) <= 1? that is, the product of all the eigenvalues are less
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