A trace inequality for matrix product

We extend to arbitrary Hermitian matrices, a well-known trace inequality for positive semidefinite matrices. When using this result for the product of two matrices when only one is Hermitian, we improve a recent trace inequality given by Fanf et al. (1994).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>