The geometric mean decomposition (Q1763844)

Let \({\mathbb C}\) be the field of complex numbers. The matrix \({\mathbb H}\) in \({\mathbb C}^{m\times m}\) is said to have a geometric mean decomposition if \({\mathbb H}\)=\textbf{QRP}\(^\star\), where \({\mathbb P}\), \({\mathbb Q}\) are matrices with orthonormal columns and \({\mathbb R}\) is a real upper triangular matrix with diagonal elements all equal to the geometric mean of the positive singular values of \({\mathbb H}\). The authors develop algorithms for computing the geometric mean decomposition of a matrix \({\mathbb H}\). The interest in this problem arose in signal processing.