Applied Linear Algebra and Matrix Analysis

ISBN-10: 0387331956
ISBN-13: 9780387331959
Edition: 2007
Authors: Thomas S. Shores
List price: $49.95
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Description: This text is intended for a one or two semester sophomore level course in linear algebra. It is designed to provide a balance of applications, theory and computation, and to emphasize their interdependence. The text has a strong orientation towards  More...

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Book details

List price: $49.95
Copyright year: 2007
Publisher: Springer
Publication date: 8/14/2007
Binding: Paperback
Pages: 384
Size: 7.00" wide x 9.00" long x 1.00" tall
Weight: 1.386
Language: English

This text is intended for a one or two semester sophomore level course in linear algebra. It is designed to provide a balance of applications, theory and computation, and to emphasize their interdependence. The text has a strong orientation towards numerical computation and the linear algebra needed in applied mathematics. At the same time, it contains a rigorous and self-contained development of most of the traditional topics in a linear algebra course. It provides background for numerous projects, which frequently require computational tools, but is not tied to any one computational platform. A comprehensive set of exercises and projects is included.

Linear Systems of Equations
Some Examples
Notation and a Review of Numbers
Gaussian Elimination: Basic Ideas
Gaussian Elimination: General Procedure
Computational Notes and Projects
Matrix Algebra
Matrix Addition and Scalar Multiplication
Matrix Multiplication
Applications of Matrix Arithmetic
Special Matrices and Transposes
Matrix Inverses
Basic Properties of Determinants
Computational Notes and Projects
Vector Spaces
Definitions and Basic Concepts
Subspaces
Linear Combinations
Subspaces Associated with Matrices and Operators
Bases and Dimension
Linear Systems Revisited
Computational Notes and Projects
Geometrical Aspects of Standard Spaces
Standard Norm and Inner Product
Applications of Norms and Inner Products
Orthogonal and Unitary Matrices
Change of Basis and Linear Operators
Computational Notes and Projects
The Eigenvalue Problem
Definitions and Basic Properties
Similarity and Diagonalization
Applications to Discrete Dynamical Systems
Orthogonal Diagonalization
Schur Form and Applications
The Singular Value Decomposition
Computational Notes and Projects
Geometrical Aspects of Abstract Spaces
Normed Spaces
Inner Product Spaces
Gram-Schmidt Algorithm
Linear Systems Revisited
Operator Norms
Computational Notes and Projects
Table of Symbols
Solutions to Selected Exercises
References
Index

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