Elementary Linear Algebra

Elementary Linear Algebra

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Description

For a sophomore-level course in Linear Algebra.



Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications. Throughout the text, use of technology is encouraged. The focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. Although matrix-oriented, the text provides a solid coverage of vector spaces
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Product details

  • Hardback | 656 pages
  • 206 x 261 x 30mm | 1,380g
  • Pearson
  • Upper Saddle River, NJ, United States
  • English
  • 2nd edition
  • 0131871412
  • 9780131871410
  • 2,262,467

Back cover copy

Elementary Linear Algebra, 2/e -- Lawrence Spence, Arnold Insel, and Stephen Friedberg



Embracing the recommendations of the Linear Algebra Curriculum Study Group, the authors have written a text that students will find both accessible and enlightening. Written for a matrix-oriented course, students from a variety of disciplines can expect a greater understanding of the concepts of linear algebra.

Starting with matrices, vectors, and systems of linear equations, the authors move towards more advanced material, including linear independence, subspaces, and bases. The authors also encourage the use of technology, either computer software (MATLAB) or super-calculators, freeing students from tedious computations so they are better able to focus on the conceptual understanding of linear algebra.

Lastly, students will find a variety of applications to engage their interest, demonstrated via economics, traffic flow, anthropology, Google searches, computer graphics, or music to name a few. By leveraging technology and incorporating engaging examples and numerous practice problems and exercises, this text best serves the needs of students attempting to master linear algebra.
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Table of contents

PREFACE ix



TO THE STUDENT xv



CHAPTER 1 MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS 1

1.1 Matrices and Vectors 1

1.2 Linear Combinations, Matrix-Vector Products, and Special Matrices 11

1.3 Systems of Linear Equations 25

1.4 Gaussian Elimination 39

1.5* Applications of Systems of Linear Equations 54

1.6 The Span of a Set of Vectors 64

1.7 Linear Dependence and Linear Independence 73

Chapter 1 Review Exercises

Chapter 1 MATLAB Exercises



CHAPTER 2 MATRICES AND LINEAR TRANSFORMATIONS 90

2.1 Matrix Multiplication 90

2.2* Applications of Matrix Multiplication 101

2.3 Invertibility and Elementary Matrices 117

2.4 The Inverse of a Matrix 130

2.5* Partitioned Matrices and Block Multiplication 141

2.6* The LU Decomposition of a Matrix 147

2.7 Linear Transformations and Matrices 162

2.8 Composition and Invertibility of Linear Transformations 175

Chapter 2 Review Exercises

Chapter 2 MATLAB Exercises



CHAPTER 3 DETERMINANTS 192

3.1 Cofactor Expansion 192

3.2 Properties of Determinants 204

Chapter 3 Review Exercises

Chapter 3 MATLAB Exercises



CHAPTER 4 SUBSPACES AND THEIR PROPERTIES 218

4.1 Subspaces 218

4.2 Basis and Dimension 232

4.3 The Dimension of Subspaces Associated with a Matrix 245

4.4 Coordinate Systems 254

4.5 Matrix Representations of Linear Operators 266

Chapter 4 Review Exercises

Chapter 4 MATLAB Exercises



CHAPTER 5 EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION 282

5.1 Eigenvalues and Eigenvectors 282

5.2 The Characteristic Polynomial 291

5.3 Diagonalization of Matrices 302

5.4* Diagonalization of Linear Operators 314

5.5* Applications of Eigenvalues 323

Chapter 5 Review Exercises

Chapter 5 MATLAB Exercises



CHAPTER 6 ORTHOGONALITY 347

6.1 The Geometry of Vectors 347

6.2 Orthogonal Vectors 360

6.3 Orthogonal Projections 374

6.4 Least-Squares Approximations and Orthogonal Projections 388

6.5 Orthogonal Matrices and Operators 398

6.6 Symmetric Matrices 412

6.7* Singular Value Decomposition 425

6.8* Principal Component Analysis 443

6.9* Rotations of R3 and Computer Graphics 452

Chapter 6 Review Exercises

Chapter 6 MATLAB Exercises



CHAPTER 7 VECTOR SPACES 473

7.1 Vector Spaces and Their Subspaces 473

7.2 Linear Transformations 485

7.3 Basis and Dimension 495

7.4 Matrix Representations of Linear Operators 505

7.5 Inner Product Spaces 517

Chapter 7 Review Exercises

Chapter 7 MATLAB Exercises



APPENDICES 534

A Sets 534

B Functions 536

C Complex Numbers 539

D Matlab 544

E The Uniqueness of the Reduced Row Echelon Form 558

REFERENCES 561

ANSWERS TO SELECTED EXERCISES 562

LIST OF FREQUENTLY USED SYMBOLS 608

INDEX 609
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Rating details

11 ratings
3.09 out of 5 stars
5 9% (1)
4 36% (4)
3 18% (2)
2 27% (3)
1 9% (1)
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