Explicit polar decomposition of complex matrices

Abstract

In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, Linear Algebra Appl., 38:239–249, 1981], the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig’s formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with rank at least n − 1.