Linear Algebra and Its Applications

Peter D. Lax

• Publisher: Wiley-Interscience
• Year: 2013
• Print ISBN: 9780471751564
• eBook ISBN: 9781118626924
• Edition: 2
• Topic: Mathematics
• Subtopic: Linear Algebra
• Index: Mathematics

This set features Linear Algebra and Its Applications, Second Edition (978-0-471-75156-4)
Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:

• The QR algorithm for finding the eigenvalues of a self-adjoint matrix
• The Householder algorithm for turning self-adjoint matrices into tridiagonal form
• The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space

Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices. Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.
and Functional Analysis (978-0-471-55604-6) both by Peter D. Lax.

Table of contents

• Cover
• Contents
• The Wiley Bicentennial-Knowledge for Generations
• Title Page
• Copyright
• Preface
• Preface to the First Edition
• Chapter 1: Fundamentals
• Chapter 2: Duality
• Chapter 3: Linear Mappings
• Chapter 4: Matrices
• Chapter 5: Determinant and Trace
• Chapter 6: Spectral Theory
• Chapter 7: Euclidean Structure
• Chapter 8: Spectral Theory of Self-Adjoint Mappings
• Chapter 9: Calculus of Vector- and Matrix-Valued Functions
• Chapter 10: Matrix Inequalities
• Chapter 11: Kinematics and Dynamics
• Chapter 12: Convexity
• Chapter 13: The Duality Theorem
• Chapter 14: Normed Linear Spaces
• Chapter 15: Linear Mappings Between Normed Linear Spaces
• Chapter 16: Positive Matrices
• Chapter 17: How to Solve Systems of Linear Equations
• Chapter 18: How to Calculate the Eigenvalues of Self-Adjoint Matrices
• Solutions of Selected Exercises
• Bibliography
• Appendix 1: Special Determinants
• Appendix 2: The Pfaffian
• Appendix 3: Symplectic Matrices
• Appendix 4: Tensor Product
• Appendix 5: Lattices
• Appendix 6: Fast Matrix Multiplication
• Appendix 7: Gershgorin’s Theorem
• Appendix 8: The Multiplicity of Eigenvalues
• Appendix 9: The Fast Fourier Transform
• Appendix 10: The Spectral Radius
• Appendix 11: The Lorentz Group
• Appendix 12: Compactness of the Unit Ball
• Appendix 13: A Characterization of Commutators
• Appendix 14: Liapunov’s Theorem
• Appendix 15: The Jordan Canonical Form
• Appendix 16: Numerical Range
• Index