Journal of Convex Analysis 16 (2009), No. 2, 617--632
Copyright Heldermann Verlag 2009
Morphisms of Normal Decomposition Systems
Department of Applied Mathematics and Computer Science, University of Liefe Sciences, Akademicka 13, 20-950 Lublin, Poland
A normal decomposition (ND) system is an algebraic structure connected with a decomposition statement for vectors of a linear space and with a variational inequality related to the decomposition [see e.g. A. S. Lewis, SIAM J. Matrix Anal. Appl. 17 (1996) 927--947]. The Singular Value Decomposition for complex matrices and the trace inequality of von Neumann provide an example of an ND system. In this paper, we study morphisms and homomorphisms of ND systems. Applications for eigenvalues and to singular values of matrices are given.
Keywords: Linear operator, weak majorization, G-majorization, GIC ordering, eigenvalue, singular value, Eaton system, normal decomposition system, group induced cone ordering, morphism, homomorphism, partial isometry.
MSC: 15A30, 15A39; 15A18, 15A42
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