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.
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.