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.

*Proof*

too short to write

in a comment.

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And thus, if you treat as a local expert,

]]>For the positive definite imaginary part, I am still a bit confused. The imaginary part of does not even seem to be Hermitian. But I think I see how to get the conclusion that follows anyway: The eigenvalues above have positive imaginary part . Using the fact that has an orthogonal eigenbasis, you can now calculate that the has a nonnegative imaginary part for any .

Is this what it means for the imaginary part of $\latex R$ to be positive definite?

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