Perturbation bounds on the polar decomposition

The polar decomposition of ann ×n-matrixA takes the formA=MH whereM is orthogonal andH is symmetric and positive semidefinite. This paper presents strict bounds, (with no order terms), on the perturbationsM,H ofM andH respectively, whenA is perturbed byA. The bounds onM can also be applied to the orthogonal Procrustes problem.