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 -