
Journal of Convex Analysis 14 (2007), No. 1, 035048 Copyright Heldermann Verlag 2007 GMajorization Inequalities and Canonical Forms of Matrices Marek Niezgoda Dept. of Applied Mathematics, Agricultural University, Akademicka 13, 20950 Lublin, Poland marek.niezgoda@ar.lublin.pl 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 Gmajorization 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. Gdoubly stochastic operators are discussed. Keywords: Gmajorization, Eaton system, normal decomposition system, finite reflection group, Gdoubly stochastic operator, eigenvalue, singular value. MSC: 15A18, 15A21; 15A42, 15A30 [ Fulltextpdf (138 KB)] for subscribers only. 