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