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The Wishart distribution is a common matrix distribution on square symmetric semi-definite matrices.

8 votes

Distribution of the sum of Wishart distributed random matrices

Depending on what you mean by closed-form, the answer is to some extent, yes. As per my comment, if $\Psi_1=\Psi_2$, then it can be shown that $A = A_1+A_2$ follows a Wishart distribution with scale m …
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