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Procrustes problems in finite dimensional indefinite scalar product spaces

โœ Scribed by Ulric Kintzel

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
364 KB
Volume
402
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Some applications from multidimensional scaling in an environment of indefinite scalar products are investigated. In particular, the construction of points from given distances is considered, and two variants of Procrustes problems are discussed. It is found that both Procrustes problems can be solved with the help of H-polar decompositions or (G, H)-polar decompositions of specified matrices. Furthermore, a method for the numerical computation of H-or (G, H)-polar decompositions of nonsingular matrices is described.

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Continuity properties of factors in polar decompositions of matrices with respect to indeยฎnite scalar products are studied. The matrix having the polar decomposition and the indeยฎnite scalar product are allowed to vary. Closely related properties of a self-adjoint (with respect to an indeยฎnite scala