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

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