On some matrix inequalities.
The paper reproves the arithmetic-geometric mean inequality of \textit{R. Bhatia} and \textit{F. Kittaneh} [SIAM J. Matrix Anal. Appl. 11, No. 2, 272--277 (1990; Zbl 0704.47014)] in two equivalent versions via Weyl's monotonicity principle and a cleverly designed block matrix representaion for the inequality. The arithmetic-geometric mean inequality is then applied to quickly prove a generalization of the trace inequality of \textit{T. W. Anderson} and \textit{J. B. Taylor} [Linear Algebra Appl. 30, 93--99 (1980; Zbl 0434.15017)] to matrices, as well as a generalization to two matrices of the norm inequality of \textit{F. Kittaneh} [J. Funct. Anal. 143, No. 2, 337--348 (1997; Zbl 0959.47005)] that originally involved only one matrix.
scientific article; zbMATH DE number 2012715