Elementary Linear Algebra with Supplemental Applications
International Student Version
10th Edition
Published on 10. August 2010
Book
Paperback/Softback
848 pages
978-0-470-56157-7 (ISBN)
Description
Elementary Linear Algebra 10th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Technology also is not required, but for those who would like to use MATLAB, Maple, or Mathematica, or calculators with linear algebra capabilities, exercises are included at the ends of chapters that allow for further exploration using those tools.
More details
Persons
Content
ELEMENTARY LINEAR ALGEBRA WITH APPLICATIONS
10TH EDITION
CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES
1.1. Introduction to Systems of Linear Equations
1.2. Gaussian Elimination
1.3. Matrices and Matrix Operations
1.4. Inverses; Algebraic Properties of Matrices
1.5. Elementary Matrices and a Method for Finding A-1
1.6. More on Linear Systems and Invertible Matrices
1.7. Diagonal, Triangular, and Symmetric Matrices
1.8. Applications of Linear Systems (Traffic flow
Electrical Networks; Balancing Chemical Equations, Polynomial Interpolation
1.9. Leontief Input-Output Models
* Chapter Summary
CHAPTER 2 DETERMINANTS
2.1. Determinants by Cofactor Expansion
2.2. Evaluating Determinants by Row Reduction
2.3. Properties of Determinants; Adjoint; Cramer's Rule
Chapter Summary
CHAPTER 3 EUCLIDEAN VECTOR SPACES
3.1. Vectors in 2-space, 3-space, and n-space
3.2. Norm, Dot Product, and Distance in Rn
3.3. Orthogonality
3.4. The Geometry of Linear Systems
3.5. Cross Product
* Chapter Summary
CHAPTER 4 GENERAL VECTOR SPACES
4.1. Real Vector Spaces
4.2. Subspaces
4.3. Linear Independence
4.4. Coordinates and Basis
4.5. Dimension
4.6. Change of Basis
4.7. Row Space, Column Space, and Null Space
4.8. Rank, Nullity, and the Fundamental Matrix Spaces
4.9 Linear Transformations from Rn to Rm
4.10. Properties of Matrix Transformations from Rn to Rm
4.11. Geometry of Matrix Operators
4.12. Dynamical Systems and Markov Chains
* Chapter Summary
CHAPTER 5 EIGNVALUES AND EIGENVECTORS
5.1. Eigenvalues and Eigenvectors
5.2. Diagonalization
5.3. Complex Vector Spaces
5.4. Application to Differential Equations
* Chapter Summary
CHAPTER 6 INNER PRODUCT SPACES
6.1. Inner Products
6.2. Angle and Orthogonality in Inner Product Spaces
6.3. Orthonormal Bases; Gram-Schmidt Process; QR - Decomposition
6.4. Best Approximation; Least Squares
6.5. Least Squares Fitting to Data
6.6. Fourier Series
* Chapter Summary
CHAPTER 7 DIAGONALIZATION AND QUADRATIC FORMS
7.1. Orthogonal Matrices
7.2. Orthogonal Diagonalization
7.3. Quadratic Forms
7.4. Application of Quadratic Forms to Optimization
7.5. Hermitian, Unitary, and Normal Matrices
* Chapter Summary
CHAPTER 8 LINEAR TRANSFORMATIONS
8.1. General Linear Transformations
8.2. Isomorphism
8.3. Composition and Inverse Transformations
8.4. Matrices of General Linear Transformations
8.5. Similarity
* Chapter Summary
CHAPTER 9 NUMERICAL METHODS
9.1. Matrix Factorization and LU-Decompositions
9.2. The Power Method
9.3. Application to Internet Search Engines
9.4. Comparison of Procedures for Solving Linear Systems
9.5. Singular-Value Decomposition
9.6. Application of Singular Value Decomposition to Data Compression
* Chapter Summary
CHAPTER 10 APPLICATIONS OF LINEAR ALGEBRA
10.1 Constructing Curves and Surfaces through Specified Points
10.2 Geometric Linear Programming
10.3 The Earliest Applications of Linear Algebra
10.4 Cubic Spline Interpolation
10.5 Graph Theory
10.6 Games of Strategy
10.7 Forest Management
10.8 Equilibrium Temperature Distributions
10.9 Computed Tomography
10.10 Fractals
10.11 Chaos
10.12 Cryptography
10.13 Genetics
10.14 Age-Specific Population Growth
10.15 Harvesting of Animal Populations
10.16 A Least Squares Model for Human Hearing
10.17 Warps and Morphs
APPENDIX A How to Read Theorems
APPENDIX B Complex Numbers
10TH EDITION
CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES
1.1. Introduction to Systems of Linear Equations
1.2. Gaussian Elimination
1.3. Matrices and Matrix Operations
1.4. Inverses; Algebraic Properties of Matrices
1.5. Elementary Matrices and a Method for Finding A-1
1.6. More on Linear Systems and Invertible Matrices
1.7. Diagonal, Triangular, and Symmetric Matrices
1.8. Applications of Linear Systems (Traffic flow
Electrical Networks; Balancing Chemical Equations, Polynomial Interpolation
1.9. Leontief Input-Output Models
* Chapter Summary
CHAPTER 2 DETERMINANTS
2.1. Determinants by Cofactor Expansion
2.2. Evaluating Determinants by Row Reduction
2.3. Properties of Determinants; Adjoint; Cramer's Rule
Chapter Summary
CHAPTER 3 EUCLIDEAN VECTOR SPACES
3.1. Vectors in 2-space, 3-space, and n-space
3.2. Norm, Dot Product, and Distance in Rn
3.3. Orthogonality
3.4. The Geometry of Linear Systems
3.5. Cross Product
* Chapter Summary
CHAPTER 4 GENERAL VECTOR SPACES
4.1. Real Vector Spaces
4.2. Subspaces
4.3. Linear Independence
4.4. Coordinates and Basis
4.5. Dimension
4.6. Change of Basis
4.7. Row Space, Column Space, and Null Space
4.8. Rank, Nullity, and the Fundamental Matrix Spaces
4.9 Linear Transformations from Rn to Rm
4.10. Properties of Matrix Transformations from Rn to Rm
4.11. Geometry of Matrix Operators
4.12. Dynamical Systems and Markov Chains
* Chapter Summary
CHAPTER 5 EIGNVALUES AND EIGENVECTORS
5.1. Eigenvalues and Eigenvectors
5.2. Diagonalization
5.3. Complex Vector Spaces
5.4. Application to Differential Equations
* Chapter Summary
CHAPTER 6 INNER PRODUCT SPACES
6.1. Inner Products
6.2. Angle and Orthogonality in Inner Product Spaces
6.3. Orthonormal Bases; Gram-Schmidt Process; QR - Decomposition
6.4. Best Approximation; Least Squares
6.5. Least Squares Fitting to Data
6.6. Fourier Series
* Chapter Summary
CHAPTER 7 DIAGONALIZATION AND QUADRATIC FORMS
7.1. Orthogonal Matrices
7.2. Orthogonal Diagonalization
7.3. Quadratic Forms
7.4. Application of Quadratic Forms to Optimization
7.5. Hermitian, Unitary, and Normal Matrices
* Chapter Summary
CHAPTER 8 LINEAR TRANSFORMATIONS
8.1. General Linear Transformations
8.2. Isomorphism
8.3. Composition and Inverse Transformations
8.4. Matrices of General Linear Transformations
8.5. Similarity
* Chapter Summary
CHAPTER 9 NUMERICAL METHODS
9.1. Matrix Factorization and LU-Decompositions
9.2. The Power Method
9.3. Application to Internet Search Engines
9.4. Comparison of Procedures for Solving Linear Systems
9.5. Singular-Value Decomposition
9.6. Application of Singular Value Decomposition to Data Compression
* Chapter Summary
CHAPTER 10 APPLICATIONS OF LINEAR ALGEBRA
10.1 Constructing Curves and Surfaces through Specified Points
10.2 Geometric Linear Programming
10.3 The Earliest Applications of Linear Algebra
10.4 Cubic Spline Interpolation
10.5 Graph Theory
10.6 Games of Strategy
10.7 Forest Management
10.8 Equilibrium Temperature Distributions
10.9 Computed Tomography
10.10 Fractals
10.11 Chaos
10.12 Cryptography
10.13 Genetics
10.14 Age-Specific Population Growth
10.15 Harvesting of Animal Populations
10.16 A Least Squares Model for Human Hearing
10.17 Warps and Morphs
APPENDIX A How to Read Theorems
APPENDIX B Complex Numbers