The \(\psi_S\) polar decomposition
Let \(S\) be a nonsingular \(n\) by \(n\) complex matrix. The authors define \(\psi_S(A)\) for \(A\) being nonsingular and singular, respectively. It is proved that every nonsingular \(A\) has a \(\psi_S\) polar decomposition \(A=RE\), where \(R\) is \(\psi_S\) orthogonal and \(E\) is \(\psi_S\) symmetric. The authors also determine which singular matrices have a \(\psi_S\) polar decomposition.
scientific article; zbMATH DE number 5602608