Title Matrix inequalities and their extensions in lie groups / Tin-Yau Tam, Xuhua Liu.
Imprint Boca Raton, FL : CRC Press, 2018.


 Internet  Electronic Book    AVAILABLE
Edition First edition.
Description 1 online resource
Series Chapman & Hall/CRC research notes in mathematics series
Chapman & Hall/CRC research notes in mathematics series.
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
Subject Matrix inequalities.
Lie groups.
Contents Cover; Half Title; Title; Copyright; Dedication; Contents; Preface; Chapter 1 Review of Matrix Theory; Matrix Decompositions; Polar Decompositions; Singular Value Decomposition; QR Decomposition; Cholesky Decomposition; Additive Decompositions; Jordan Decompositions; LU Decomposition; L U Decomposition; Majorizations; Matrix Norms; The Matrix Exponential Map; Compound Matrices and Applications; Compound Matrices; Additive Compound Matrices; Applications to Matrix Inequalities; Chapter 2 Structure Theory of Semisimple Lie Groups; Smooth Manifolds; Lie Groups and Their Lie Algebras.
Complex Semisimple Lie AlgebrasReal Forms; Cartan Decompositions; Root Space Decomposition; Iwasawa Decompositions; Weyl Groups; KA+K Decomposition; Complete Multiplicative Jordan Decomposition; Kostant's Preorder; Chapter 3 Inequalities for Matrix Exponentials; Golden-Thompson Inequality; Araki-Lieb-Thirring Inequality; Bernstein Inequality; Extensions to Lie Groups; Chapter 4 Inequalities for Spectral Norm; Matrix Inequalities for Spectral Norm; Extensions to Lie Groups; Chapter 5 Inequalities for Unitarily Invariant Norms; Matrix Inequalities for Unitarily Invariant Norms.
Extensions to Lie GroupsChapter 6 Inequalities for Geometric Means; Matrix Inequalities for Geometric Means; Symmetric Spaces; Extensions to Lie Groups; Geodesic Triangles in Symmetric Spaces; Chapter 7 Kostant Convexity Theorems; Kostant Linear Convexity Theorem; A Partial Order; Thompson-Sing and Related Inequalities; Some Matrix Results Associated with SO(n) and Sp(n); Kostant Nonlinear Convexity Theorem; Thompson Theorem on Complex Symmetric Matrices; Bibliography; Index.
Summary "Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups. It is the first systematic work in the area and will appeal to linear algebraists and Lie group researchers."--Provided by publisher.
Other Author Liu, Xuhua, author.