Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 14 (2007), No. 1, 035--048
Copyright Heldermann Verlag 2007

G-Majorization Inequalities and Canonical Forms of Matrices

Marek Niezgoda
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

[ Fulltext-pdf  (138  KB)] for subscribers only.