Block-matrix generalizations of Schur's basic theorems on Hadamard products
\textit{I. Schur} [J. Reine Angew. Math. 140, 1-28 (1911; JFM 42.0367.01)] derived a series of inequalities for the eigenvalues and the singular values of the Hadamard (entrywise) product of two matrices. Motivated by some later applications of these estimations to the theory of monotone and convex matrix functions, the authors present generalizations of a variety of Schur's inequalities for Hadamard products in which both factors are conformally partitioned block matrices, and the entries of one factor are constant within one block. Since such products turn out to be special cases of a block Kronecker product, the results are given in terms of this.
scientific article; zbMATH DE number 64495