Linear Algebra and Its Applications

by Lax, Peter D.

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Title Statements

Full title :Linear Algebra and Its Applications.

Summary

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.

Edition Statements

Publication Date:©2008
Edition:2nd ed

Publication Statements

Publisher(s):John Wiley & Sons, Incorporated
Place of Publication:Chicester
Language:eng
Publication Date:©2008

The Physical Object

Description:1 online resource (306 pages).

Edition Identifiers

ISBN:9781118626924, 1118626923
oclc:on1044732797
LC Classification:QA184.2 .L38 2013
Dewey Decimal:512/.5

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 …