Skip to main content Skip to main navigation
  1. Home
  2. Computer Science & IT
  3. Advanced Math
  4. Linear Algebra
  5. Linear Algebra with Applications (Subscription)

Linear Algebra with Applications, 9th edition

  • Steven J. Leon

Published by Pearson (July 30th 2014) - Copyright © 2015

9th edition

Chosen format
View all
Linear Algebra with Applications (Subscription)

ISBN-13: 9780321983961

Includes: eText
Instant access
$44.99

What's included

  • eText

    A digital version of the text you can personalize and read online or offline.

Overview

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book.

This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.

 

This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra.

Table of contents

Preface

What’s New in the Eighth Edition?

Computer Exercises

Overview of Text

Suggested Course Outlines

Supplementary Materials

Acknowledgments

 

1. Matrices and Systems of Equations

1.1 Systems of Linear Equations

1.2 Row Echelon Form

1.3 Matrix Arithmetic

1.4 Matrix Algebra

1.5 Elementary Matrices

1.6 Partitioned Matrices

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

2. Determinants

2.1 The Determinant of a Matrix

2.2 Properties of Determinants

2.3 Additional Topics and Applications

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

3. Vector Spaces

3.1 Definition and Examples

3.2 Subspaces

3.3 Linear Independence

3.4 Basis and Dimension

3.5 Change of Basis

3.6 Row Space and Column Space

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

4. Linear Transformations

4.1 Definition and Examples

4.2 Matrix Representations of Linear Transformations

4.3 Similarity

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

5. Orthogonality

5.1 The Scalar Product in Rn

5.2 Orthogonal Subspaces

5.3 Least Squares Problems

5.4 Inner Product Spaces

5.5 Orthonormal Sets

5.6 The Gram—Schmidt Orthogonalization Process

5.7 Orthogonal Polynomials

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

6. Eigenvalues

6.1 Eigenvalues and Eigenvectors

6.2 Systems of Linear Differential Equations

6.3 Diagonalization

6.4 Hermitian Matrices

6.5 The Singular Value Decomposition

6.6 Quadratic Forms

6.7 Positive Definite Matrices

6.8 Nonnegative Matrices

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

7. Numerical Linear Algebra

7.1 Floating-Point Numbers

7.2 Gaussian Elimination

7.3 Pivoting Strategies

7.4 Matrix Norms and Condition Numbers

7.5 Orthogonal Transformations

7.6 The Eigenvalue Problem

7.7 Least Squares Problems

            Matlab Exercises

            Chapter Test A

            Chapter Test B

 

Appendix: MATLAB

The MATLAB Desktop Display

Basic Data Elements

Submatrices

Generating Matrices

Matrix Arithmetic

MATLAB Functions

Programming Features

M-files

Relational and Logical Operators

Columnwise Array Operators

Graphics

Symbolic Toolbox

Help Facility

Conclusions

 

Bibliography

A. Linear Algebra and Matrix Theory

B. Applied and Numerical Linear Algebra

C. Books of Related Interest

 

Answers to Selected Exercises

For teachers

All the material you need to teach your courses.

Discover teaching material