Majorizations and inequalities in matrix theory
type: Item
instance of: scholarly article
title: Majorizations and inequalities in matrix theory
zbMATH Open document ID: 0798.15024
DOI: 10.1016/0024-3795(94)90341-7
author: V. Pereyra
published in: Linear Algebra and its Applications
publication date: 1994-11-06T00:00:00Z
review text: This article is an excellent survey of results related to majorization in matrix theory since the appearance of the book ``Inequalities: theory of majorization and its applications'' (1979; Zbl 0437.26007) by \textit{A. W. Marshall} and \textit{I. Olkin}. This survey consists of eight sections: 1) Majorization for sequences, 2) Majorization for matrices, 3) Matrix means, 4) Matrix inequalities, 5) Log majorization, 6) Spectral perturbation, 7) Hadamard products and 8) Majorizations in von Neumann algebras. A great number of recent references are also given.
reviewed by: Silvestru Sever Dragomir
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15-02
zbMATH DE Number: 566090
zbMATH Keywords: survey article
zbMATH Keywords: matrix means
zbMATH Keywords: matrix inequalities
zbMATH Keywords: log majorization
zbMATH Keywords: spectral perturbation
zbMATH Keywords: majorization
zbMATH Keywords: Hadamard products
zbMATH Keywords: von Neumann algebras
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90341-7
OpenAlex ID: W2058041395
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cites work: Q5611281
cites work: Q5581719
cites work: Series and parallel addition of matrices
cites work: Symmetric function means of positive operators
cites work: Q4169818
cites work: Concavity of certain maps on positive definite matrices and applications to Hadamard products
cites work: Hua—Marcus inequalities
cites work: Q3314407
cites work: Totally positive matrices
cites work: On some operator inequalities
cites work: Comparison of norms \(|||f(A)-f(B)|||\) and \(|||f(|A-B|)|||\)
cites work: Majorization, doubly stochastic matrices, and comparison of eigenvalues
cites work: Q4283112
cites work: Q4839467
cites work: Eigenvalue inequalities associated with the cartesian decomposition
cites work: Log majorization and complementary Golden-Thompson type inequalities
cites work: Inequality between powers of positive semidefinite matrices
cites work: Q3824896
cites work: Q3352005
cites work: Q3973561
cites work: Induced norms of the Schur multiplier operator
cites work: Triangular truncation and finding the norm of a Hadamard multiplier
cites work: Majorzation and singular values
cites work: Majorization and Singular Values II
cites work: Majorization and singular values. III
cites work: On majorization and Schur products
cites work: Inequalities for the Trace of Matrix Exponentials
cites work: Inequalities between means of positive operators
cites work: Q3996765
cites work: A generalization of the Hoffman-Wielandt theorem
cites work: A bound for the spectral variation of a unitary operator
cites work: More Matrix Forms of the Arithmetic-Geometric Mean Inequality
cites work: A softer, stronger Lidskii theorem
cites work: Q4072380
cites work: Hermitian Matrix Inequalities and a Conjecture
cites work: Spectral inequalities for matrix exponentials
cites work: An operator inequality
cites work: Norms of Hadamard Multipliers
cites work: Q4721086
cites work: Lipschitz Continuity of Functions of Operators in the Schatten Classes
cites work: Q5593024
cites work: Q4839471
cites work: Non-commutative Banach function spaces
cites work: Q4405419
cites work: A note on the Hoffman-Wielandt theorem
cites work: Q3955927
cites work: Generalized s-numbers of \(\tau\)-measurable operators
cites work: Über eine Ungleichung für positiv definite Matrizen
cites work: Matrices Sous-Stochastiques et Fonctions Convexes
cites work: Balayage Defined by the Nonnegative Convex Functions
cites work: Furuta's inequality and its application to Ando's theorem
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cites work: Inequalities for Symmetric Functions and Hermitian Matrices

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cites work: THE EIGEN- AND SINGULAR VALUES OF THE SUM AND PRODUCT OF LINEAR OPERATORS

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cites work: Q4735664

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cites work: Hölder-type norm inequalities for Schur products of matrices

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cites work: Q3857325

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