TITLE:
Matrices That Commute with Their Conjugate and Transpose
AUTHORS:
Geoffrey Goodson
KEYWORDS:
Normal Matrix; Matrix Commuting with Its Conjugate and Transpose
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.3 No.3,
September
17,
2013
ABSTRACT:
It is known that if A∈Mn is normal (AA*=A*A) , then AA ̄=A ̄A if and only if AAT=ATA. This leads to the question: do both AA ̄=A ̄A and AAT=ATAimply that Ais normal? We give an
example to show that this is false when n=4, but we show that it is true when n=2and n=3.