Linear Algebra and Its Applications

ISBN-10: 0471751561
ISBN-13: 9780471751564
Edition: 2nd 2007 (Revised)
Authors: Peter D. Lax
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Description: 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,  More...

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Book details

List price: $100.00
Edition: 2nd
Copyright year: 2007
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/10/2007
Binding: Hardcover
Pages: 392
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 2.002

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.

Preface
Preface to the First Edition
Fundamentals
Duality
Linear Mappings
Matrices
Determinant and Trace
Spectral Theory
Euclidean Structure
Spectral Theory of Self-Adjoint Mappings of a Euclidean Space into Itself
Calculus of Vector- and Matrix-Valued Functions
Matrix Inequalities
Kinematics and Dynamics
Convexity
The Duality Theorem
Normed Linear Spaces
Linear Mappings Between Normed Linear Spaces
Positive Matrices
How to Solve Systems of Linear Equations
How to Calculate the Eigenvalues of Self-Adjoint Matrices
Solutions of Selected Exercises
Bibliography
Special Determinants
The Pfaffian
Symplectic Matrices
Tensor Product
Lattices
Fast Matrix Multiplication
Gershgorina??s Theorem
The Multiplicity of Eigenvalues
The Fast Fourier Transform
The Spectral Radius
The Lorentz Group
Compactness of the Unit Ball
A Characterization of Commutators
Liapunova??s Theorem
The Jordan Canonical Form
Numerical Range
Index
List of Series Titles

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