Morphisms of Normal Decomposition Systems

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.