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How to calculate entropy using the eigenvalues when the eigenvalues are negative?

Is there a simple relation between the entropy of a matrix and its characteristic polynomial?

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How do you define it? – Chris Godsil Jan 28 '13 at 12:41
    
the eigenvaluesof the matrix $H$ have to be real, positive and sum to unity, otherwise the entropy makes no sense. – Carlo Beenakker Jan 29 '13 at 8:30

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