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I am interested in the eigenvalue spectrum of the following matrix A A=(id+diag random) M Where M is a given matrix with a known eigenvalue spectrum, lets say for simplicity that it is Hermitian. diag random is a diagonal random matrix where each entry is an independent random gaussian number. And id is the identity matrix. For some cases of M, such as M=id this problem is very easy. But if M is more complicated than that there seem to be no clear way to explicitly write down M's spectrum. Any ideas how I could proceeed?

Thanks

W

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    This was "untagged". I've tagged it linear algebra, but I'm not sure that's appropriate. Further tag edits welcome.2012-05-22

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