Article - preprint
It is known that AB and BA are similar when A and B are Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if A is Hermitian and B is normal. Perhaps surprisingly, similarity does hold when A is positive semidefinite and B is normal.
© 2016 Elsevier Inc.
Garcia, S.R., Sherman, D., Weiss, G., On the similarity of AB and BA for normal and other matrices, Lin. Alg. Appl. 508 (2016), no. 1, 14-21.