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

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Thomas S. Shores: Applied Linear Algebra and Matrix Analysis

Published $2007$, Springer

ISBN 978-0387331959.


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


Subject Matter


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