A review of selected topics in majorization theory

Marek Niezgoda. "A review of selected topics in majorization theory." Banach Center Publications 99.1 (2013): 123-154. <http://eudml.org/doc/282065>.

@article{MarekNiezgoda2013,
abstract = {In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors are described. Generalizations of Hardy-Littlewood-Pólya Theorem and Schur-Ostrowski Theorem are presented. Generalized Schur-convex functions are investigated. Extensions of Ky Fan inequalities are provided. Applications to Grüss and Ostrowski type inequalities are given.},
author = {Marek Niezgoda},
journal = {Banach Center Publications},
keywords = {majorization; Schur-convex function; group majorization; group-induced cone ordering; Eaton triple; normal decomposition system; Schur inequality; eigenvalue; singular value; Chebyshev functional; similarly separable vectors; Chebyshev type inequality; Ky Fan type inequality; Grüss type inequality; Ostrowski type inequality},
language = {eng},
number = {1},
pages = {123-154},
title = {A review of selected topics in majorization theory},
url = {http://eudml.org/doc/282065},
volume = {99},
year = {2013},
}

TY - JOUR
AU - Marek Niezgoda
TI - A review of selected topics in majorization theory
JO - Banach Center Publications
PY - 2013
VL - 99
IS - 1
SP - 123
EP - 154
AB - In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors are described. Generalizations of Hardy-Littlewood-Pólya Theorem and Schur-Ostrowski Theorem are presented. Generalized Schur-convex functions are investigated. Extensions of Ky Fan inequalities are provided. Applications to Grüss and Ostrowski type inequalities are given.
LA - eng
KW - majorization; Schur-convex function; group majorization; group-induced cone ordering; Eaton triple; normal decomposition system; Schur inequality; eigenvalue; singular value; Chebyshev functional; similarly separable vectors; Chebyshev type inequality; Ky Fan type inequality; Grüss type inequality; Ostrowski type inequality
UR - http://eudml.org/doc/282065
ER -