Abstract
The question of whether a real matrix is symmetrizable via multiplication by a diagonal matrix with positive diagonal entries is reduced to the corresponding question for M -matrices and related to Hadamard products. In the process, for a nonsingular M -matrix A , it is shown that tr( A -1 A T ) ⩽ n , with equality if and only if A is symmetric, and that the minimum eigenvalue of A -1 ∘ A is ⩽ 1 with equality in the irreducible case if and only if A is positive diagonally symmetrizable.
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