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Overview

A thorough and accessible introduction to linear algebra, delivered digitally.
The new 10th Edition of Linear Algebra with Applications continues to encourage a challenging and broad understanding of the subject. For this edition, Steve Leon – one of the leading figures in the use of technology for linear algebra – is joined by new co-author Lisette de Pillis of Harvey Mudd College, who brings her passion for teaching and solving real-world problems to this revision.

Key to the 10th Edition was transforming from a primarily print-based resource to a digital learning tool. The eText is packed with content and tools, such as interactive figures, that help bring course content to life for students and augment instruction. This change in format supports the authors’ hallmark – using modern practical application to make key concepts tangible and demonstrating how mathematics is used in the real world.

Each chapter contains integrated worked examples, practical applications, computer exercises, and chapter tests.  The important roles played by geometry and visualization in understanding linear algebra are emphasized.

For sophomore-level or junior/senior-level first courses in linear algebra; assumes calculus as a prerequisite.

Pearson eText allows educators to easily share their own notes with students so they see the connection between their reading and what they learn in class – motivating them to keep reading, and keep learning. Portable access lets students study on the go, even offline. And, student usage analytics offer insight into how students use the eText, helping educators tailor their instruction.

NOTE: This ISBN is for the Pearson eText access card. For students purchasing this product from an online retailer, Pearson eText is a fully digital delivery of Pearson content and should only be purchased when required by your instructor. In addition to your purchase, you will need a course invite link, provided by your instructor, to register for and use Pearson eText.

0135181631 / 9780135181638 PEARSON ETEXT LINEAR ALGEBRA WITH APPLICATIONS -- ACCESS CARD, 10/e 

Table of contents

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 — True or False

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 — True or False

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 — True or False

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 — True or False

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 — True or False

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 — True or False

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

7.8 Iterative Methods

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B


8. Canonical Forms

8.1 Nilpotent Operators

8.2 The Jordan Canonical Form


Appendix: MATLAB

Bibliography

Answers to Selected Exercises

Index


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