On Matrix Trace Inequalities and Related Topics for Products of Hermitian Matrices

Alternative proofs of some simple matrix trace inequalities of Bellman [in "General Inequalities 2, Proceedings, 2nd International Conference on General Inequalities" (E. F. Beckenbach, Ed.), pp. 89-90, Birkhäuser, Basel, 1980], Neudecker [J. Math, Anal. Appl.166 (1992), 302-303], and Yang [J. Math. Anal. Appl.133 (1988), 573-574] are considered and further properties of products of Hermitian and positive (semi)definite matrices are investigated.