Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Marek Niezgoda

Department of Applied Mathematics and Computer Science, University of Life Sciences, Akademicka 13, 20-950 Lublin, Poland

marek.niezgoda@up.lublin.pl

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

Mathematics Subject Classification

15A30, 15A39; 15A18, 15A42

Suggested citation

M. Niezgoda. “Morphisms of Normal Decomposition Systems.” Journal of Convex Analysis 16 (2009), No. 2, 617–632. https://doi.org/10.68381/jca16034

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press.