Spectral inequalities and equalities involving products of matrices Original Research Article

Let A1,…,Ak be n×n matrices. We studied inequalities and equalities involving eigenvalues, diagonal entries, and singular values of A0=A1cdots, three dots, centeredAk and those of A1,…,Ak. It is shown that the matrices attaining equalities often have special reducible structure. The results are then applied to study normality and reducibility of matrices, extending some results and answering some questions of Miranda, Wang and Zhang.