Some determinantal inequalities for Hadamard product of matrices

摘要

The main result of this paper is the following: if both A = (a(ij)) and B = (b(ij)) are M-matrices or positive definite real symmetric matrices of order n, the Hadamard product of A and B is denoted by A circle B, and A(k) and B-k (k = 1, 2, n) are the k x k leading principal submatrices of A and B, respectively, then det(A circle B) greater than or equal to det(A B) Pi(k=2)(n) ( a(kk) det A(k-1)/det A(k) + b(kk) det Bk-1/det B-k -1). (C) 2003 Elsevier Science Inc. All fights reserved. [References: 8]