Elementary Linear Algebra
Pearson New International Edition
2nd Edition
Published on 29. July 2013
Book
Paperback/Softback
632 pages
978-1-292-02503-2 (ISBN)
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
More details
Edition
2nd edition
Language
English
Place of publication
Harlow
United Kingdom
Target group
College/higher education
Dimensions
Height: 275 mm
Width: 218 mm
Thickness: 26 mm
Weight
1200 gr
ISBN-13
978-1-292-02503-2 (9781292025032)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Lawrence E. Spence | Arnold J. Insel | Stephen H. Friedberg
Elementary Linear Algebra: Pearson New International Edition
Pearson New International Edition
E-Book
08/2013
1st Edition
Pearson Education Limited
€42.80
Available for download
Previous edition
Lawrence E. Spence | Arnold J. Insel | Stephen H. Friedberg
Elementary Linear Algebra
International Edition
Book
07/2007
2nd Edition
Pearson
€142.36
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Content
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 VECTOR SPACES 473
6.1 Vector Spaces and Their Subspaces 473
6.2 Linear Transformations 485
6.3 Basis and Dimension 495
6.4 Matrix Representations of Linear Operators 505
6 .5 Inner Product Spaces 517
Chapter 6 Review Exercises
Chapter 6 MATLAB Exercises
CHAPTER 7 ORTHOGONALITY 347
7.1 The Geometry of Vectors 347
7.2 Orthogonal Vectors 360
7.3 Orthogonal Projections 374
7.4 Least-Squares Approximations and Orthogonal Projections 388
7.5 Orthogonal Matrices and Operators 398
7.6 Symmetric Matrices 412
&
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 VECTOR SPACES 473
6.1 Vector Spaces and Their Subspaces 473
6.2 Linear Transformations 485
6.3 Basis and Dimension 495
6.4 Matrix Representations of Linear Operators 505
6 .5 Inner Product Spaces 517
Chapter 6 Review Exercises
Chapter 6 MATLAB Exercises
CHAPTER 7 ORTHOGONALITY 347
7.1 The Geometry of Vectors 347
7.2 Orthogonal Vectors 360
7.3 Orthogonal Projections 374
7.4 Least-Squares Approximations and Orthogonal Projections 388
7.5 Orthogonal Matrices and Operators 398
7.6 Symmetric Matrices 412
&