Simultaneous polar decomposition of rectangular complex matrices
The starting point of the present paper is the well known (left and right) polar decomposition of a complex \(m\times n\)-matrix which is in general not unique. Two complex matrices of the same size are said to be simultaneously polar decomposable if the partial isometries in their polar decompositions coincide. Now a criterion for simultaneous polar decomposibility is derived in terms of the so-called GL-ordering [cf. \textit{J. Hauke} and \textit{A. Markiewicz}, Linear Algebra Appl. 219, 187-193 (1995; Zbl 0833.15012)].
scientific article; zbMATH DE number 1331306
scientific article