Some determinantal inequalities for Hadamard product of matrices

The main result of this paper is the following: if both A=(aij) and B=(bij) are M-matrices or positive definite real symmetric matrices of order n, the Hadamard product of A and B is denoted by A B, and Ak and Bk (k=1,2,…,n) are the k×k leading principal submatrices of A and B, respectively, then