论文信息 - Closure properties of certain positivity classes of matrices under various algebraic operations

Closure properties of certain positivity classes of matrices under various algebraic operations

Abstract We present a table indicating whether or not each of five positivity classes of matrices (positive definite Hermitian matrices, M -matrices, inverse M -matrices, totally positive matrices, and inverse totally positive matrices) is closed under each of seven algebraic operations (conventional multiplication, addition, powers, extraction of roots, Hadamard multiplication, the Hadamard product of one element and the inverse of another, and LU factorization.) Three of these 35 facts seem not to have been previously known, and key examples and references are given.

Charles R. Johnson

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