A matrix trace inequality (Q5905530)

The author establishes the following theorem: If A and B are two positive semidefinite matrices of the same order then the trace of AB is non- negative and the square-root of trace AB is less or equal to the arithmetic mean of trace A and trace B. This is a slight improvement of a result by \textit{Y. Yang} [J. Math. Anal. Appl. 133, No. 2, 573-574 (1988; Zbl 0651.15018)].