Introduction to Linear Algebra

by Lee Johnson; Jimmy Thomas Arnold; R. Dean Riess

• ISBN13: 9780201824162
• ISBN10: 0201824167
• Edition: 4th
• Format: Hardcover
• Copyright: 1997-08-01
• Publisher: Pearson College Div

Summary

This book stresses both practical computation and theoretical principles and centers on the early introduction of matrix theory and systems of linear equations, elementary vector-space concepts, and the eigenvalue problem. Featuring a gradual increase in the level of difficulty, an accessible writing style, and the integration of MATLAB, this text is an excellent introduction for engineering students.

Table of Contents

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

Table of Contents provided by Publisher. All Rights Reserved.