Showing papers by "Roger A. Horn published in 2010"
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12 Jul 2010TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Abstract: 1. The field of values 2. Stable matrices and inertia 3. Singular value inequalities 4. Matrix equations and Kronecker products 5. Hadamard products 6. Matrices and functions.
7,013 citations
TL;DR: In this paper, it was shown that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than their spectral radius for positive semidefinite matrices.
Abstract: X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan's conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.
25 citations