Traces of matrix products

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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
StatePublished - Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, International Linear Algebra Society. All rights reserved. All rights reserved.


  • Random matrix
  • Trace


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