Linear Algebra and Its Applications 2nd Edition by Peter Lax 0471751561 9780471751564

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ISBN 10: 0471751561

ISBN 13: 9780471751564

Author: Peter D. Lax

Praise for the First Edition “. . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician’s bookshelf.” -American Mathematical Monthly 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.

Linear Algebra and Its Applications 2nd Table of contents:

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

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