(untitled) (Journal of Computational Mathematics, 2021)
Let A, AC^m× n, rank (A)=rank (A)=n. Suppose that A=QH and A=QH are the polar decompositions of A and A, respectively. It is proved that \|Q-Q\|_F≤ 2\|A^+\|_2\|A-A\|_F and \|H-H\|_F≤ 2\|A-A\|_F hold, where A^+ is the Moore-Penrose inverse of A, and \| \|_2 and \| \|_F denote the spectral norm and the Frobenius norm, respectively.