Some inequalities concerning positive-definite Hermitian matrices

Abstract

1. Let H = (aij) be a positive-definite Hermitian matrix of order n. For any k distinct integers i1, i2, …, ik between 1 and n, we shall use the symbol (i1, i2, …, ik) to denote the k-rowed principal submatrix of H corresponding to the rows and columns with indices i1, i2, …, ik. It is well known thatMand more generally,