Traces of matrix products

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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(A2B2) is exactly.

Original languageEnglish (US)
Pages (from-to)716-734
Number of pages19
JournalElectronic Journal of Linear Algebra
Volume27
DOIs
StatePublished - Oct 2014

Keywords

  • Random matrix
  • Trace

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