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If I have $n$ Hermitian Positive Semi-Definite matrices $A_1, A_2 ... A_n$, does there exist any type of product (viz. Kronecker, Hadamard, Tracy-Singh, etc.) that gives back a Hermitian Positive Semi-Definite matrix.

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closed as off-topic by user26857, Nosrati, Claude Leibovici, Henrik, user91500 Apr 9 '17 at 9:19

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The Kronecker product always works, because the eigenvalues of the product are necessarily non-negative. The Schur product (aka Hadamard) works, by a theorem of Schur.

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  • $\begingroup$ Thank you! I wrote a small code to generate a 100 random PSDH matrices, and do the product and check. It worked but I was looking to make sure it was mathematically sound :) $\endgroup$ – shaunakde Apr 8 '17 at 14:26

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