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New Perturbation Bounds for the Unitary Polar Factor

Authors:
Li, Ren-Cang
Technical Report Identifier: CSD-94-852
December 1994
CSD-94-852.pdf
CSD-94-852.ps

Abstract: Let A be an m x n (m >= n) complex matrix. It is known that there is a unique polar decomposition A = QH, where Q*Q = I, the n x n identity matrix, and H is positive definite, provided A has full column rank. This note addresses the following question: how much may Q change if A is perturbed? For the square case m = n our bound, which is valid for any unitarily invariant norm, is sharper and simpler than Mathias's (SIAM J. Matrix Anal. Appl., 14 (1993), 588-597.). For the non-square case, we also establish a bound for unitarily invariant norm, which has not been done in literature.