Ship-Ship-Hooray! Free Shipping on $25+ Details >

Cover type: Hardback

Edition: 3RD 96

Copyright: 1996

Publisher: Saunders College Division

Published: 1996

International: No

Edition: 3RD 96

Copyright: 1996

Publisher: Saunders College Division

Published: 1996

International: No

List price: $370.50

All of our used books are 100% hand-inspected and guaranteed! Happy you, happy us.

FREE Shipping on $25+

Order $25 or more and the shipping's on us. Marketplace items and other exclusions apply.

Ships Today!

Order by noon CST (Mon-Fri, excluding holidays). Some restrictions apply.

Easy 30-Day Returns

Not the right book for you? We accept returns within 30 days of purchase. Access codes are non-refundable once revealed or redeemed.

Ships directly from us

You Save $185.32 (50%)

$185.18

Condition: Very Good
**100% Satisfaction Guarantee**

We hand-inspect every one of our used books.

We hand-inspect every one of our used books.

Well, that's no good. Unfortunately, this edition is currently out of stock. Please check back soon.

Also available in the Marketplace starting at $12.49

Price | Condition | Seller | Comments |
---|

This book is intended for the first course in linear algebra, taken by mathematics, science, engineering and economics majors. The new edition presents a stronger geometric intuition for the ensuing concepts of span and linear independence. Applications are integrated throughout to illustrate the mathematics and to motivate the student.

Preface.

List of Applications.

**1. Introduction to Linear Equations and Matrices. **

Introduction to Linear Systems and Matrices.

Gaussian Elimination.

The Algebra of Matrices: Four Descriptions of the Product.

Inverses and Elementary Matrices.

Gaussian Elimination as a Matrix Factorization.

Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems.

Review Exercises.

**2. Determinants. **

The Determinant Function.

Properties of Determinants.

Finding det A Using Signed Elementary Products.

Cofactor Expansion: Cramer's Rule.

Applications.

Review Exercises.

**3. Vector Spaces. **

Vectors in 2- and 3-Spaces.

Euclidean n-Space.

General Vector Spaces.

Subspaces, Span, Null Spaces.

Linear Independence.

Basis and Dimension.

The Fundamental Subspaces of a Matrix; Rank.

Coordinates and Change of Basis.

An Application: Error-Correcting Codes.

Review Exercises.

Cumulative Review Exercises.

**4. Linear Transformations, Orthogonal Projections and Least Squares. **

Matrices as Linear Transformation.

Relationships Involving Inner Products.

Least Squares and Orthogonal Projections.

Orthogonal Bases and the Gram-Schmidt Process.

Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited).

Encoding the QR Decompositions: A Geometric Approach.

General Matrices of Linear of Linear Transformations; Similarity.

Review Exercises.

Cumulative Review Exercises.

**5. Eigenvectors and Eigenvalues. **

A Brief Introduction to Determinants.

Eigenvalues and Eigenvectors.

Diagonalization.

Symmetric Matrices.

An Application - Difference Equations: Fibonacci Sequences and Markov Processes.

An Application -Differential Equations.

An Application -- Quadratic Forms.

Solving the Eigenvalue Problem Numerically.

Review Exercises.

Cumulative Review Exercises.

**6. Further Directions. Function Spaces. **

The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems.

Iterative Method. Matrix Norms.

General Vector Spaces and Linear Transformations Over an Arbitrary Field.

Review Exercises.

Appendix A: More on LU Decompositions.

Appendix B: Counting Operations and Gauss-Jordan Elimination.

Appendix C: Another Application.

Appendix D: Introduction to MATLAB and Projects.

Bibliography and Further Readings.

Index.

shop us with confidence

Summary

This book is intended for the first course in linear algebra, taken by mathematics, science, engineering and economics majors. The new edition presents a stronger geometric intuition for the ensuing concepts of span and linear independence. Applications are integrated throughout to illustrate the mathematics and to motivate the student.

Table of Contents

Preface.

List of Applications.

**1. Introduction to Linear Equations and Matrices. **

Introduction to Linear Systems and Matrices.

Gaussian Elimination.

The Algebra of Matrices: Four Descriptions of the Product.

Inverses and Elementary Matrices.

Gaussian Elimination as a Matrix Factorization.

Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems.

Review Exercises.

**2. Determinants. **

The Determinant Function.

Properties of Determinants.

Finding det A Using Signed Elementary Products.

Cofactor Expansion: Cramer's Rule.

Applications.

Review Exercises.

**3. Vector Spaces. **

Vectors in 2- and 3-Spaces.

Euclidean n-Space.

General Vector Spaces.

Subspaces, Span, Null Spaces.

Linear Independence.

Basis and Dimension.

The Fundamental Subspaces of a Matrix; Rank.

Coordinates and Change of Basis.

An Application: Error-Correcting Codes.

Review Exercises.

Cumulative Review Exercises.

**4. Linear Transformations, Orthogonal Projections and Least Squares. **

Matrices as Linear Transformation.

Relationships Involving Inner Products.

Least Squares and Orthogonal Projections.

Orthogonal Bases and the Gram-Schmidt Process.

Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited).

Encoding the QR Decompositions: A Geometric Approach.

General Matrices of Linear of Linear Transformations; Similarity.

Review Exercises.

Cumulative Review Exercises.

**5. Eigenvectors and Eigenvalues. **

A Brief Introduction to Determinants.

Eigenvalues and Eigenvectors.

Diagonalization.

Symmetric Matrices.

An Application - Difference Equations: Fibonacci Sequences and Markov Processes.

An Application -Differential Equations.

An Application -- Quadratic Forms.

Solving the Eigenvalue Problem Numerically.

Review Exercises.

Cumulative Review Exercises.

**6. Further Directions. Function Spaces. **

The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems.

Iterative Method. Matrix Norms.

General Vector Spaces and Linear Transformations Over an Arbitrary Field.

Review Exercises.

Appendix A: More on LU Decompositions.

Appendix B: Counting Operations and Gauss-Jordan Elimination.

Appendix C: Another Application.

Appendix D: Introduction to MATLAB and Projects.

Bibliography and Further Readings.

Index.

Publisher Info

Publisher: Saunders College Division

Published: 1996

International: No

Published: 1996

International: No

Preface.

List of Applications.

**1. Introduction to Linear Equations and Matrices. **

Introduction to Linear Systems and Matrices.

Gaussian Elimination.

The Algebra of Matrices: Four Descriptions of the Product.

Inverses and Elementary Matrices.

Gaussian Elimination as a Matrix Factorization.

Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems.

Review Exercises.

**2. Determinants. **

The Determinant Function.

Properties of Determinants.

Finding det A Using Signed Elementary Products.

Cofactor Expansion: Cramer's Rule.

Applications.

Review Exercises.

**3. Vector Spaces. **

Vectors in 2- and 3-Spaces.

Euclidean n-Space.

General Vector Spaces.

Subspaces, Span, Null Spaces.

Linear Independence.

Basis and Dimension.

The Fundamental Subspaces of a Matrix; Rank.

Coordinates and Change of Basis.

An Application: Error-Correcting Codes.

Review Exercises.

Cumulative Review Exercises.

**4. Linear Transformations, Orthogonal Projections and Least Squares. **

Matrices as Linear Transformation.

Relationships Involving Inner Products.

Least Squares and Orthogonal Projections.

Orthogonal Bases and the Gram-Schmidt Process.

Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited).

Encoding the QR Decompositions: A Geometric Approach.

General Matrices of Linear of Linear Transformations; Similarity.

Review Exercises.

Cumulative Review Exercises.

**5. Eigenvectors and Eigenvalues. **

A Brief Introduction to Determinants.

Eigenvalues and Eigenvectors.

Diagonalization.

Symmetric Matrices.

An Application - Difference Equations: Fibonacci Sequences and Markov Processes.

An Application -Differential Equations.

An Application -- Quadratic Forms.

Solving the Eigenvalue Problem Numerically.

Review Exercises.

Cumulative Review Exercises.

**6. Further Directions. Function Spaces. **

The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems.

Iterative Method. Matrix Norms.

General Vector Spaces and Linear Transformations Over an Arbitrary Field.

Review Exercises.

Appendix A: More on LU Decompositions.

Appendix B: Counting Operations and Gauss-Jordan Elimination.

Appendix C: Another Application.

Appendix D: Introduction to MATLAB and Projects.

Bibliography and Further Readings.

Index.