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Schur’s theorem for a block Hadamard product

2012; Elsevier BV; Volume: 437; Issue: 3 Linguagem: Inglês

10.1016/j.laa.2012.04.002

1873-1856

Michael Günther, Lutz Klotz,

Matrix Theory and Algorithms

We define a generalized Kronecker product for block matrices, mention some of its properties, and apply it to the study of a block Hadamard product of positive semidefinite matrices, which was defined by Horn, Mathias, and Nakamura. Under strong commutation assumptions we obtain generalizations of Schur’s theorem and of Oppenheim’s inequality.