Lax Linear Algebra and Its Applications

2. Auflage 2013
ISBN: 978-1-118-62692-4
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 392 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

Praise for the First Edition
". . .recommended for the teacher and researcher as well as forgraduate students. In fact, [it] has a place on everymathematician's bookshelf." -American Mathematical Monthly
Linear Algebra and Its Applications, Second Edition presents linearalgebra as the theory and practice of linear spaces and linear mapswith a unique focus on the analytical aspects as well as thenumerous applications of the subject. In addition to thoroughcoverage of linear equations, matrices, vector spaces, game theory,and numerical analysis, the Second Edition featuresstudent-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 finitedimensional vector spaces, and subsequent chapters addressconvexity and the duality theorem as well as describe the basics ofnormed linear spaces and linear maps between normed spaces.
Further updates and revisions have been included to reflect themost up-to-date coverage of the topic, including:
* The QR algorithm for finding the eigenvalues of a self-adjointmatrix
* The Householder algorithm for turning self-adjoint matricesinto tridiagonal form
* The compactness of the unit ball as a criterion of finitedimensionality of a normed linear space
Additionally, eight new appendices have been added and cover topicssuch as: the Fast Fourier Transform; the spectral radius theorem;the Lorentz group; the compactness criterion for finitedimensionality; the characterization of commentators; proof ofLiapunov's stability criterion; the construction of the JordanCanonical form of matrices; and Carl Pearcy's elegant proof ofHalmos' conjecture about the numerical range of matrices.
Clear, concise, and superbly organized, Linear Algebra and ItsApplications, Second Edition serves as an excellent text foradvanced undergraduate- and graduate-level courses in linearalgebra. Its comprehensive treatment of the subject also makes itan ideal reference or self-study for industry professionals.

Autoren/Hrsg.

Lax, Peter D.

Inhaltsverzeichnis

Preface.
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 Self-Adjoint Mappings.
9. Calculus of Vector- and Matrix-Valued 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 Self-AdjointMatrices.
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.

Über Autor(innen)

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.