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• W1969752991 abstract "We are interested in the calculation of explicit formulae for the condition numbers of the two factors of the polar decomposition of a full rank real or complex m × n matrix A, where m ≥ n. We use a unified presentation that enables us to compute such condition numbers in the Frobenius norm, in cases where A is a square or a rectangular matrix subjected to real or complex perturbations. We denote by σ1 (respectively σ n) the largest (respectively smallest) singular value of A, and by K(A) = σ1/σ n the generalized condition number of A. Our main results are that the absolute condition number of the Hermitian polar factor is √2(1 + K(A)2)1/2/(1 + K(A)) and that the absolute condition number of the unitary factor of a rectangular matrix is 1/σ n. Copyright © 2000 John Wiley & Sons, Ltd." @default.
• W1969752991 created "2016-06-24" @default.
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• W1969752991 date "2000-01-01" @default.
• W1969752991 modified "2023-10-11" @default.
• W1969752991 title "On the condition numbers associated with the polar factorization of a matrix" @default.
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• W1969752991 doi "https://doi.org/10.1002/1099-1506(200007/08)7:5<337::aid-nla200>3.0.co;2-4" @default.
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