Traces of matrix products

John Greene

doi:10.13001/1081-3810.1999

Traces of matrix products

John Greene

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Pages (from-to)	716-734
Number of pages	19
Journal	Electronic Journal of Linear Algebra
Volume	27
DOIs	https://doi.org/10.13001/1081-3810.1999
State	Published - Oct 2014

Bibliographical note

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

Keywords

Random matrix
Trace

Publisher link

10.13001/1081-3810.1999

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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{\textquoteright}s and B{\textquoteright}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.",

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AB - 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.

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JF - Electronic Journal of Linear Algebra

ER -

Traces of matrix products

Abstract

Bibliographical note

Keywords

Publisher link

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