Some inequalities concerning positive-definite Hermitian matrices

Abstract

1. Let H = ( a ij ) be a positive-definite Hermitian matrix of order n . For any k distinct integers i 1 , i 2 , …, i k between 1 and n , we shall use the symbol ( i 1 , i 2 , …, i k ) to denote the k -rowed principal submatrix of H corresponding to the rows and columns with indices i 1 , i 2 , …, i k . It is well known thatM and more generally,