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Introduction to Linear Algebra

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

Introduction to Linear Algebra

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

ISBN 13:
9780201824162
ISBN 10:
0201824167
Edition: 4th
Format: Hardcover
Copyright: 08/01/1997
Publisher: Pearson College Div
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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.

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.

Amazon no longer offers textbook rentals. We do!

Introduction to Linear Algebra

Introduction to Linear Algebra

9780201824162

0201824167

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Introduction to Linear Algebra

Introduction to Linear Algebra

9780201824162

0201824167

Summary

Table of Contents

Supplemental Materials

Write a Review

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