Geodesic
G-Majorization Inequalities and Canonical Forms of Matrices
Journal of convex analysis, Tome 14 (2007) no. 1, pp. 35-48

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An Eaton system is connected with a decomposition statement for vectors of a linear space and with a scalar inequality related to the decomposition. The Singular Value Decomposition for the space of complex matrices associated with von Neumann's trace inequality is a typical example. We present a G-majorization inequality involving two orthoprojectors related to an Eaton system. The inequality generalizes a variety of majorization results on eigenvalues and singular values of matrices. A relationship between the inequality and canonical form theorems for certain spaces of matrices is shown. G-doubly stochastic operators are discussed.
Classification : 15A18, 15A21, 15A42, 15A30
Mots-clés : G-majorization, Eaton system, normal decomposition system, finite reflection group, G-doubly stochastic operator, eigenvalue, singular value 
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     title = {G-Majorization {Inequalities} and {Canonical} {Forms} of {Matrices}},
     journal = {Journal of convex analysis},
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     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_1_JCA_2007_14_1_a3/}
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M. Niezgoda. G-Majorization Inequalities and Canonical Forms of Matrices. Journal of convex analysis, Tome 14 (2007) no. 1, pp. 35-48. http://geodesic.mathdoc.fr/item/JCA_2007_14_1_JCA_2007_14_1_a3/