IJPAM: Volume 50, No. 4 (2009)

A PROOF OF HADAMARD INEQUALITY FOR
NONSINGULAR OR POSITIVE DEFINITE MATRICES

Sumitra Purkayastha
Bayesian and Interdisciplinary Research Unit
Indian Statistical Institute
203, B.T. Road, Kolkata, 700 108, INDIA
e-mail: sumitra@isical.ac.in

Abstract.Hadamard inequality for nonsingular matrices states the following: if is an nonsingular matrix, then This result is equivalent to the following fact about positive definite matrices: if is an positive definite matrix, then We provide a simple proof of this later fact that uses in a straightforward manner spectral decomposition of a positive definite matrix and the inequality between arithmetic mean and geometric mean of a set of positive numbers.