Journal of Convex Analysis 14 (2007), No. 1, 035--048
Copyright Heldermann Verlag 2007
G-Majorization Inequalities and Canonical Forms of Matrices
Dept. of Applied Mathematics, Agricultural University, Akademicka 13, 20-950 Lublin, Poland
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.
Keywords: G-majorization, Eaton system, normal decomposition system, finite reflection group, G-doubly stochastic operator, eigenvalue, singular value.
MSC: 15A18, 15A21; 15A42, 15A30
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