Polar Decompositions, Factor Analysis and Procrustes Problems in Finite Dimensional Indefinite Scalar Product Spaces
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Author(s) : Ulric Kintzel

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 32-2003

MSC 2000

15A63 Quadratic and bilinear forms, inner products
15A23 Factorization of matrices

Abstract :
A criterion for the existence of H-polar decompositions based on comparing canonical forms is presented, and a numerical procedure is explained for computing H-polar decompositions of a matrix for which the product of itself with its H-adjoint is diagonalisable. Furthermore, the H-orthogonal or H-unitary procrustes problem is stated, and solved by application of H-polar decompositions.

Keywords : Indefinite scalar products, polar decompositions, factor analysis, procrustes problems