TY - JOUR

T1 - Traces of matrix products

AU - Greene, John

PY - 2014/10

Y1 - 2014/10

N2 - 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.

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.

KW - Random matrix

KW - Trace

UR - http://www.scopus.com/inward/record.url?scp=84910665288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84910665288&partnerID=8YFLogxK

U2 - 10.13001/1081-3810.1999

DO - 10.13001/1081-3810.1999

M3 - Article

AN - SCOPUS:84910665288

VL - 27

SP - 716

EP - 734

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

SN - 1081-3810

ER -