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Linear Algebra with Applications, 10th edition

  • Steve Leon
  • Lisette de Pillis
Pearson eText Linear Algebra with Applications -- Instant Access

ISBN-13: 9780135240960

Includes: eText (12-month access)

10th edition

Published byPearson (September 15th 2020) - Copyright © 2020

Instant access
$59.99
Instant access
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Overview

Linear Algebra with Applications provides a thorough and accessible introduction to linear algebra that uses  modern practical applications to make key concepts tangible and demonstrate how math 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.

Pearson eText is an easy-to-use digital textbook that you can read online or offline. Make it your own by adding highlights and notes, and learn on the go with the mobile app. At the end of your subscription, you can opt to renew access to your eText and personalized notes.

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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