# Linear Algebra and Its Applications, Volume 10

John Wiley & Sons, Sep 10, 2007 - Mathematics - 376 pages

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.

### What people are saying -Write a review

User Review - Flag as inappropriate

Excellent. Not at all introductory. I use it for important topics not in the official curriculum.

User Review - Flag as inappropriate

Presents advanced material in a way that avoids overly messy generalizations. A great reference book if you need to get work done. Also the proofs are very nicely explained. Highly recommended.

### Contents

 Fundamentals 1 Duality 13 Linear Mappings 19 Matrices 32 Determinant and Trace 44 Spectral Theory 58 Euclidean Structure 77 Spectral Theory of SelfAdjoint Mappings 101
 Positive Matrices 237 How to Solve Systems of Linear Equations 246 How to Calculate the Eigenvalues of SelfAdjoint Matrices 262 Solutions 278 Bibliography 300 Symplectic Matrices 308 Lattices 317 Gershgorins Theorem 323

 Calculus of Vector and MatrixValued Functions 121 Matrix Inequalities 143 Kinematics and Dynamics 172 Convexity 187 The Duality Theorem 202 Normed Linear Spaces 214 Linear Mappings Between Normed Linear Spaces 229
 The Spectral Radius 334 The Lorentz Group 342 Compactness of the Unit Ball 352 The Jordan Canonical Form 363 Index 373 Copyright