Book:Thomas S. Shores/Applied Linear Algebra and Matrix Analysis

Thomas S. Shores: Applied Linear Algebra and Matrix Analysis

Published $\text {2007}$, Springer

ISBN 978-0387331959

This book is part of the Undergraduate Texts in Mathematics series.

Subject Matter

• Linear Algebra

Contents

1 LINEAR SYSTEMS OF EQUATIONS

1.1 Some Examples

1.2 Notation and a Review of Numbers

1.3 Gaussian Elimination: Basic Ideas

1.4 Gaussian Elimination: General Procedure

1.5 *Computational Notes and Projects

2 MATRIX ALGEBRA

2.1 Matrix Addition and Scalar Multiplication

2.2 Matrix Multiplication

2.3 Applications of Matrix Arithmetic

2.4 Special Matrices and Transposes

2.5 Matrix Inverses

2.6 Basic Properties of Determinants

2.7 *Computational Notes and Projects

3 VECTOR SPACES

3.1 Definitions and Basic Concepts

3.2 Subspaces

3.3 Linear Combinations

3.4 Subspaces Associated with Matrices and Operators

3.5 Bases and Dimension

3.6 Linear Systems Revisited

3.7 *Computational Notes and Projects

4 GEOMETRICAL ASPECTS OF STANDARD SPACES

4.1 Standard Norm and Inner Product

4.2 Applications of Norms and Inner Products

4.3 Orthogonal and Unitary Matrices

4.4 *Change of Basis and Linear Operators

4.5 *Computational Notes and Projects

5 THE EIGENVALUE PROBLEM

5.1 Definitions and Basic Properties

5.2 Similarity and Diagonalization

5.3 Applications to Discrete Dynamical Systems

5.4 Orthogonal Diagonalization

5.5 *Schur Form and Applications

5.6 *The Singular Value Decomposition

5.7 *Computational Notes and Projects

6 GEOMETRICAL ASPECTS OF ABSTRACT SPACES

6.1 Normed Spaces

6.2 Inner Product Spaces

6.3 Gram–Schmidt Algorithm

6.4 Linear Systems Revisited

6.5 *Operator Norms

6.6 *Computational Notes and Projects

Table of Symbols

Solutions to Selected Exercises

References

Index