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Some inequalities concerning positive-definite Hermitian matrices

Published online by Cambridge University Press:  24 October 2008

Ky Fan
The American University and University of Notre Dame


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 thatM

and more generally,

Research Article
Copyright © Cambridge Philosophical Society 1955

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