An alternative derivation of the polar decomposition (Q1572718)

This work provides an elementary derivation of the decomposition of deformation gradient tensor in continuum mechanics. Polar decomposition is valid for all square matrices, not only for the deformation gradients. It simply states that any square matrix is expressible as product of an orthogonal matrix (incidentally, this orthogonal matrix is not skew-symmetric as is claimed by the author) and a symmetric matrix. The decomposition is unique if the matrix is regular. The author could have found a very short proof of this theorem given by \textit{J. L. Ericksen} [Tensor Analysis, Appendix, \textit{S. Flugge}, Handbuch der Physik. Band III/1: Prinzipien der klassischen Mechanik und Feldtheorie. Encyclopedia of physics. Vol. III/1: Principles of classical mechanics and field theory. (German). Berlin-Göttingen-Heidelberg: Springer-Verlag VII (1960; Zbl 0118.39702)].