Abstract
In a classic 1911 paper, I. Schur gave several useful bounds for the spectral norm and eigenvalues of the Hadamard (entrywise) product of two matrices. Motivated by applications to the theory of monotone and convex matrix functions, we are led to consider Hadamard products in which both factors are conformally partitioned block matrices and the entries of one factor are constant within each block. Such products are special cases of a block Kronecker (tensor) product, and it is in this context that we present generalizations of Schur's results.
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