An Analytic Approach To a Permanent Conjecture
Linear Algebra and its Applications
Hadamard product, Irreducible matrix, Lagrange multiplier, Maximizing matrix, Permanent
This paper is concerned with the conjecture on the permanent of the Hadamard product of two positive semidefinite matrices: per(A∘B)≼perAperB. We present some properties of correlation matrices and introduce an analytic approach of maximizing matrices for the permanent conjecture. Given an irreducible correlation matrix, we show that its maximizing matrix is (i) singular, (ii) irreducible, and (iii) invariant by a row and column reduction.
Zhang, Fuzhen, "An Analytic Approach To a Permanent Conjecture" (2013). Mathematics Faculty Articles. 26.