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Elementary Linear Algebra with Applications, Ninth Edition

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Elementary Linear Algebra with Applications, Ninth Edition

by Bernard Kolman; David R. Hill

Publisher: Pearson

Copyright Year: 2008

Publishing Date: 2007/05/03

eText ISBN-10: 0-13-208286-1

eText ISBN-13: 978-0-13-208286-0

Print ISBN-10: 0-13-229654-3

Print ISBN-13: 978-0-13-229654-0

Course: Mechanical Engineering, Introductory Linear Algebra

Pages: 720

eTextbook $69.33

(180 day subscription)

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Table of Contents | Description

Instructor Resources | Student Resources

ABOUT THIS TITLE - TABLE OF CONTENTS

To the Student, xvii

1. Linear Equations and Matrices, 1

1.1. Systems of Linear Equations, 1

1.2. Matrices, 11

1.3. Matrix Multiplication, 21

1.4. Algebraic Properties of Matrix Operations, 34

1.5. Special Types of Matrices and Partitioned Matrices, 42

1.6. Matrix Transformations, 55

1.7. Computer Graphics (Optional), 63

1.8. Correlation Coefficient (Optional), 73

Supplementary Exercises, 80

2. Solving Linear Systems, 86

2.1. Echelon Form of a Matrix, 86

2.2. Solving Linear Systems, 95

2.3. Elementary Matrices; Finding A^{−1}, 117

2.4. Equivalent Matrices, 126

2.5. LU-Factorization (Optional), 130

Supplementary Exercises, 137

3. Determinants, 141

3.1. Definition, 141

3.2. Properties of Determinants, 146

3.3. Cofactor Expansion, 157

3.4. Inverse of a Matrix, 165

3.5. Other Applications of Determinants, 169

3.6. Determinants from a Computational Point of View, 172

Supplementary Exercises, 174

4. Real Vector Spaces, 177

4.1. Vectors in the Plane and in 3-Space, 177

4.2. Vector Spaces, 188

4.3. Subspaces, 197

4.5. Linear Independence, 216

4.6. Basis and Dimension, 229

4.7. Homogeneous Systems, 244

4.8. Coordinates and Isomorphisms, 253

4.9. Rank of a Matrix, 270

Supplementary Exercises, 285

5. Inner Product Spaces, 290

5.1. Length and Direction in R^2 and R^3, 290

5.2. Cross Product in R^3 (Optional), 299

5.3. Inner Product Spaces, 307

5.4. Gram–Schmidt Process, 320

5.5. Orthogonal Complements, 332

5.6. Least Squares (Optional), 350

Supplementary Exercises, 358

6. Linear Transformations and Matrices, 363

6.1. Definition and Examples, 363

6.2. Kernel and Range of a Linear Transformation, 375

6.3. Matrix of a Linear Transformation, 389

6.4. Vector Space of Matrices and Vector Space of Linear Transformations (Optional), 399

6.5. Similarity, 407

6.6. Introduction to Homogeneous Coordinates (Optional), 414

Supplementary Exercises, 430

7. Eigenvalues and Eigenvectors, 436

7.1. Eigenvalues and Eigenvectors, 436

7.2. Diagonalization and Similar Matrices, 453

7.3. Diagonalization of Symmetric Matrices, 463

Supplementary Exercises, 477

8. Applications of Eigenvalues and Eigenvectors (Optional), 481

8.1. Stable Age Distribution in a Population; Markov Processes (Optional), 481

8.2. Spectral Decomposition and Singular Value Decomposition, 488

8.3. Dominant Eigenvalue and Principal Component Analysis (Optional), 501

8.4. Differential Equations, 515

8.5. Dynamical Systems, 525

8.6. Real Quadratic Forms, 535

8.7. Conic Sections, 544

8.8. Quadric Surfaces, 552

9. MATLAB for Linear Algebra, 561

9.1. Input and Output in MATLAB, 562

9.2. Matrix Operations in MATLAB, 567

9.3. Matrix Powers and Some Special Matrices, 570

9.4. Elementary Row Operations in MATLAB, 573

9.5. Matrix Inverses in MATLAB, 583

9.6. Vectors in MATLAB, 584

9.7. Applications of Linear Combinations in MATLAB, 586

9.8. Linear Transformations in MATLAB, 590

9.9. MATLAB Command Summary, 592

10. MATLAB Exercises, 597

Appendix A. Preliminaries, A-1

A.2. Functions, A-1

Appendix B. Complex Numbers, A-5

B.1. Complex Numbers, A-5

B.2. Complex Numbers in Linear Algebra, A-13

Appendix C. Introduction to Proofs, A-22

C.1. Logic, A-22

C.2. Techniques of Proof, A-27

Glossary for Linear Algebra, A-31

Answers to Odd-Numbered Exercises, A-37

Page Index to Lemmas, Theorems, and Corollaries, I-11

Photo Credits, P-1

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ABOUT THIS TITLE - DESCRIPTION

For introductory sophomore-level courses in Linear Algebra or Matrix Theory. This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.

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