Home > ELA > Vol. 27 (2014)
Article Title
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} .
Recommended Citation
Greene, John.
(2014),
"Traces of Matrix Products",
Electronic Journal of Linear Algebra,
Volume 27.
DOI: https://doi.org/10.13001/1081-3810.1999
abs_vol27_pp716-734.pdf (21 kB)
Abstract
Abstract