Ebook
Linear Algebra and Its Applications, 2nd EditionISBN: 9781118626924
392 pages
May 2013

Description
". . .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 studentfriendly 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 uptodate coverage of the topic, including:
 The QR algorithm for finding the eigenvalues of a selfadjoint
matrix
 The Householder algorithm for turning selfadjoint matrices into tridiagonal form
 The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space
Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate and graduatelevel courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or selfstudy for industry professionals.
Table of Contents
Preface to the First Edition.
1. Fundamentals.
2. Duality.
3. Linear Mappings.
4. Matrices.
5. Determinant and Trace.
6. Spectral Theory.
7. Euclidean Structure.
8. Spectral Theory of SelfAdjoint Mappings.
9. Calculus of Vector and MatrixValued Functions.
10. Matrix Inequalities.
11. Kinematics and Dynamics.
12. Convexity.
13. The Duality Theorem.
14. Normed Linear Spaces.
15. Linear Mappings Between Normed Linear Spaces.
16. Positive Matrices.
17. How to Solve Systems of Linear Equations.
18. How to Calculate the Eigenvalues of SelfAdjoint Matrices.
19. Solutions.
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.
Author Information
Peter D. Lax, PhD, is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences at New York University. Dr. Lax is the recipient of the Abel Prize for 2005 "for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions". * A student and then colleague of Richard Courant, Fritz John, and K. O. Friedrichs, he is considered one of the world's leading mathematicians. He has had a long and distinguished career in pure and applied mathematics, and with over fifty years of experience in the field, he has made significant contributions to various areas of research, including integratable systems, fluid dynamics, and solitonic physics, as well as mathematical and scientific computing.
The Wiley Advantage
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
Clear, concise, and superbly organized, this new edition is an excellent text for advanced undergraduate and graduate courses and also serves as a handy professional reference.
Further updates and revisions have been included to reflect the most uptodate coverage of the topic, including:

The QR algorithm for finding the eigenvalues of a selfadjoint matrix

The Householder algorithm for turning selfadjoint 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.
Selected solutions to exercises are provided at the end of the book.
Numerous new exercises and eight new appendices have been added.