The geometric mean decomposition

Given a complex matrix H, we consider the decomposition H = QRP* where Q and P have orthonormal columns, and R is a real upper triangular matrix with diagonal elements equal to the geometric mean of the positive singular values of H. This decomposition, which we call the geometric mean decomposition, has application to signal processing and to the design of telecommunication networks. The unitary matrices correspond to information lossless filters applied to transmitted and received signals that minimize the maximum error rate of the network. Another application is to the construction of test matrices with specified singular values.