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Introduction to Linear Algebra

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ISBN-10: 0201824167

ISBN-13: 9780201824162

Edition: 4th 1998

Authors: Lee W. Johnson, R. Dean Riess, Jimmy T. Arnold

List price: $116.00
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Description:

This widely used text offers a consistent level of difficulty and an early and careful introduction to Eigenvalues, a topic that students often struggle with.
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Book details

List price: $116.00
Edition: 4th
Copyright year: 1998
Publisher: Addison-Wesley Longman, Incorporated
Publication date: 6/23/1997
Binding: Hardcover
Pages: 560
Size: 8.00" wide x 9.75" long x 1.00" tall
Weight: 2.288
Language: English

Matrices and Systems of Linear Equations
Introduction to Matrices and Systems of Linear Equations
Echelon Form and Gauss-Jordan Elimination
Consistent Systems of Linear Equations
Applications (Optional)
Matrix Operations
Algebraic Properties of Matrix Operations
Linear Independence and Nonsingular Matrices
Data Fitting, Numerical Integration, and Numerical Differentiation (Optional)
Matrix Inverses and Their Properties
Vectors in 2-Space and 3-Space
Vectors in the Plane
Vectors in Space
The Dot Product and the Cross Product
Lines and Planes in Space
The Vector Space Rn
Introduction
Vector Space Properties of Rn
Examples of Subspaces
Bases for Subspaces
Dimension
Orthogonal Bases for Subspaces
Linear Transformations from Rn to Rm
Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting
Theory and Practice of Least Squares
The Eigenvalue Problem
The Eigenvalue Problem for (2 x 2) Matrices
Determinants and the Eigenvalue Problem
Elementary Operations and Determinants (Optional)
Eigenvalues and the Characteristic Polynomial
Eigenvectors and Eigenspaces
Complex Eigenvalues and Eigenvectors
Similarity Transformations and Diagonalization
Difference Equations
Markov Chains, Systems of Differential Equations (Optional)
Vector Spaces and Linear Transformations
Introduction
Vector Spaces
Subspaces
Linear Independence, Bases, and Coordinates
Dimension
Inner-Product Spaces, Orthogonal Bases, and Projections (Optional)
Linear Transformations
Operations with Linear Transformations
Matrix Representations for Linear Transformations
Change of Basis and Diagonalization
Determinants
Introduction
Cofactor Expansions of Determinants
Elementary Operations and Determinants
Cramer's Rule
Applications of Determinants: Inverses and Wronksians
Eigenvalues and Applications
Quadratic Forms
Systems of Differential Equations
Transformation to Hessenberg Form
Eigenvalues of Hessenberg Matrices
Householder Transformations
The QR Factorization and Least-Squares Solutions
Matrix Polynomials and the Cayley-Hamilton Theorem
Generalized Eigenvectors and Solutions of Systems of Differential Equations
Appendix: An Introduction to MATLAB
Answers to Selected Odd-Numbered Exercises
Index