same and the iteration reduces to Heron's method on the singular values. This basic iteration may be refined to speed up the process: See also Cartan decomposition Algebraic polar decomposition Polar decomposition of a complex measure Lie group decomposition References Conway, J.B.: A Course in Functional Analysis. Graduate Texts in Mathematics. New York: Springer 1990 Douglas, R.G.: On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space. Proc. Amer. Math. Soc. 17, 413-415 (1966) . Lie groups Operator theory Matrix theory Matrix decompositions