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Keywords

Random matrix, Trace

Abstract

Given two noncommuting matrices, A and B, it is well known that AB and BA have the same trace. This extends to cyclic permutations of products of A’s and B’s. It is shown here that for 2×2 matrices A and B, whose elements are independent random variables with standard normal distributions, the probability that Tr(ABAB) > Tr(AB) is exactly 1/\sqrt{2} .

abs_vol27_pp716-734.pdf (21 kB)
Abstract

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