Geodesic
Morphisms of Normal Decomposition Systems
Journal of convex analysis, Tome 16 (2009) no. 2, pp. 617-632.

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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.
Classification : 15A30, 15A39, 15A18, 15A42
Mots-clés : Linear operator, weak majorization, G-majorization, GIC ordering, eigenvalue, singular value, Eaton system, normal decomposition system, group induced cone ordering, morphism, homomorphism, partial isometry 
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     title = {Morphisms of {Normal} {Decomposition} {Systems}},
     journal = {Journal of convex analysis},
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     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a17/}
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M. Niezgoda. Morphisms of Normal Decomposition Systems. Journal of convex analysis, Tome 16 (2009) no. 2, pp. 617-632. http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a17/