Finite-Dimensional Linear Algebra

Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.

The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes readers through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra).

Features

Explores various applications of linear algebra, including polynomial interpolation, graph and coding theory, linear and integer programming, linear ordinary differential equations, Lagrange multipliers, and much more

Presents important concepts and methods from numerical linear algebra

Contains a range of exercises in each section, including some that can be solved using a computer package such as MATLAB®

Incorporates mini-projects that encourage readers to develop topics not covered in the text

This book gives readers a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.