The aim of this book is to present a substantial part of matrix analysis that is functional analytic in spirit. Much of this will be of interest to graduate students and research workers in operator theory, operator algebras, mathematical physics, and numerical analysis. The book can be used as a basic text for graduate courses on advanced linear algebra and matrix analysis. It can also be used as supplementary text for courses in operator theory and numerical analysis. Among topics covered are the theory of majorization, variational principles of eigenvalues, operator monotone and convex functions, perturbation of matrix functions, and matrix inequalities. Much of this is presented for the first time in a unified way in a textbook. The reader will learn several powerful methods and techniques of wide applicability, and see connections with other areas of mathematics. A large selection of matrix inequalities will make this book a valuable reference for students and researchers who are working in numerical analysis, mathematical physics and operator theory 本书旨在为读者提供泛函分析的精髓矩阵分析.算子理论, 算子代数, 数学物理和数值分析专业的研究生和科研人员将对这本书感兴趣.本书可以作为高等线性代数和矩阵分析方向的研究生基础教程, 也可以作为算子理论和数值分析方向的补充教程

zlibzh/no-category/RAJENDRA BHATIA, Rajendra Bhatia著, Atia Bh, ( YIN ) BA DI YA, (印) 巴蒂亚著/MATRIX ANALYSIS_38081058.pdf

Matrix analysis / monograph

矩阵分析 英文

World Publishing Corporation

World Publishing Company

北京:世界图书北京出版公司

世界图书出版公司北京公司

数学研究生教{OCLCbr#E6}{OCLCbr#9D}?, Beijing, 2011, ©1997

China, People's Republic, China

Ying yin ban, Beijing, 2011

Di 1 ban, 2011-04

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Bookmarks: p1 (p1): Ⅰ A Review of Linear Algebra
p1-1 (p1): Ⅰ.1 Vector Spaces and Inner Product Spaces
p1-2 (p3): Ⅰ.2 Linear Operators and Matrices
p1-3 (p9): Ⅰ.3 Direct Sums
p1-4 (p12): Ⅰ.4 Tensor Products
p1-5 (p16): Ⅰ.5 Symmetry Classes
p1-6 (p20): Ⅰ.6 Problems
p1-7 (p26): Ⅰ.7 Notes and References
p2 (p28): Ⅱ Majorisation and Doubly Stochastic Matrices
p2-1 (p28): Ⅱ.1 Basic Notions
p2-2 (p36): Ⅱ.2 Birkhoff's Theorem
p2-3 (p40): Ⅱ.3 Convex and Monotone Functions
p2-4 (p48): Ⅱ.4 Binary Algebraic Operations and Majorisation
p2-5 (p50): Ⅱ.5 Problems
p2-6 (p54): Ⅱ.6 Notes and References
p3 (p57): Ⅲ Variational Principles for Eigenvalues
p3-1 (p57): Ⅲ.1 The Minimax Principle for Eigenvalues
p3-2 (p62): Ⅲ.2 Weyl's Inequalities
p3-3 (p65): Ⅲ.3 Wielandt's Minimax Principle
p3-4 (p68): Ⅲ.4 Lidskii's Theorems
p3-5 (p73): Ⅲ.5 Eigenvalues of Real Parts and Singular Values
p3-6 (p75): Ⅲ.6 Problems
p3-7 (p78): Ⅲ.7 Notes and References
p4 (p84): Ⅳ Symmetric Norms
p4-1 (p84): Ⅳ.1 Norms on Cn
p4-2 (p91): Ⅳ.2 Unitarily Invariant Norms on Operators on Cn
p4-3 (p98): Ⅳ.3 Lidskii's Theorem (Third Proof)
p4-4 (p101): Ⅳ.4 Weakly Unitarily Invariant Norms
p4-5 (p107): Ⅳ.5 Problems
p4-6 (p109): Ⅳ.6 Notes and References
p5 (p112): Ⅴ Operator Monotone and Operator Convex Functions
p5-1 (p112): Ⅴ.1 Definitions and Simple Examples
p5-2 (p117): Ⅴ.2 Some Characterisations
p5-3 (p123): Ⅴ.3 Smoothness Properties
p5-4 (p131): Ⅴ.4 Loewner's Theorems
p5-5 (p147): Ⅴ.5 Problems
p5-6 (p149): Ⅴ.6 Notes and References
p6 (p152): Ⅵ Spectral Variation of Normal Matrices
p6-1 (p153): Ⅵ.1 Continuity of Roots of Polynomials
p6-2 (p155): Ⅵ.2 Hermitian and Skew-Hermitian Matrices
p6-3 (p159): Ⅵ.3 Estimates in the Operator Norm
p6-4 (p165): Ⅵ.4 Estimates in the Frobenius Norm
p6-5 (p168): Ⅵ.5 Geometry and Spectral Variation:the Operator Norm.
p6-6 (p173): Ⅵ.6 Geometry and Spectral Variation:wui Norms
p6-7 (p181): Ⅵ.7 Some Inequalities for the Determinant
p6-8 (p184): Ⅵ.8 Problems
p6-9 (p190): Ⅵ.9 Notes and References
p7 (p194): Ⅶ Perturbation of Spectral Subspaces of Normal Matrices
p7-1 (p195): Ⅶ.1 Pairs of Subspaces
p7-2 (p203): Ⅶ.2 The Equation AX－XB=Y
p7-3 (p211): Ⅶ.3 Perturbation of Eigenspaces
p7-4 (p212): Ⅶ.4 A Perturbation Bound for Eigenvalues
p7-5 (p213): Ⅶ.5 Perturbation of the Polar Factors
p7-6 (p216): Ⅶ.6 Appendix: Evaluating the (Fourier) constants
p7-7 (p221): Ⅶ.7 Problems
p7-8 (p223): Ⅶ.8 Notes and References
p8 (p226): Ⅷ Spectral Variation of Nonnormal Matrices
p8-1 (p227): Ⅷ.1 General Spectral Variation Bounds
p8-2 (p238): Ⅷ.4 Matrices with Real Eigenvalues
p8-3 (p240): Ⅷ.5 Eigenvalues with Symmetries
p8-4 (p244): Ⅷ.6 Problems
p8-5 (p249): Ⅷ.7 Notes and References
p9 (p253): Ⅸ A Selection of Matrix Inequalities
p9-1 (p253): Ⅸ.1 Some Basic Lemmas
p9-2 (p255): Ⅸ.2 Products of Positive Matrices
p9-3 (p258): Ⅸ.3 Inequalities for the Exponential Function
p9-4 (p262): Ⅸ.4 Arithmetic-Geometric Mean Inequalities
p9-5 (p266): Ⅸ.5 Schwarz Inequalities
p9-6 (p271): Ⅸ.6 The Lieb Concavity Theorem
p9-7 (p275): Ⅸ.7 Operator Approximation
p9-8 (p279): Ⅸ.8 Problems
p9-9 (p285): Ⅸ.9 Notes and References
p10 (p289): Ⅹ Perturbation of Matrix Functions
p10-1 (p289): Ⅹ.1 Operator Monotone Functions
p10-2 (p296): Ⅹ.2 The Absolute Value
p10-3 (p301): Ⅹ.3 Local Perturbation Bounds
p10-4 (p310): Ⅹ.4 Appendix: Differential Calculus
p10-5 (p317): Ⅹ.5 Problems
p10-6 (p320): Ⅹ.6 Notes and References
p11 (p325): References
p12 (p339): Index

2024-06-13