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I have a question about Wishart random variable. If X follows a Wishart distribution, then does X-Y follows a Wishart Distribution if Y is a Hermitian matrix?

Thanks.

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  • $\begingroup$ that would be a socalled "noncentral Wishart distribution" $\endgroup$
    – Carlo Beenakker
    Commented Sep 24, 2013 at 12:06

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Wishart distribution is a distribution on the set of non-negative definite matrices. Since X-Y can have negative eigenvalues I'll say no.

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