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Elementary Linear Algebra, 11th Edition

Book Description

Elementary Linear Algebra: Applications Version, 11th 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.

Table of Contents

  1. COVER
  2. TITLE PAGE
  3. About the Author
  4. Preface
  5. CHAPTER 1 Systems of Linear Equations and Matrices
    1. 1.1 Introduction to Systems of Linear Equations
    2. 1.2 Gaussian Elimination
    3. 1.3 Matrices and Matrix Operations
    4. 1.4 Inverses; Algebraic Properties of Matrices
    5. 1.5 Elementary Matrices and a Method for Finding A−1
    6. 1.6 More on Linear Systems and Invertible Matrices
    7. 1.7 Diagonal,Triangular, and Symmetric Matrices
    8. 1.8 MatrixTransformations
    9. 1.9 Applications of Linear Systems
    10. 1.10 Leontief Input-Output Models
  6. CHAPTER 2 Determinants
    1. 2.1 Determinants by Cofactor Expansion
    2. 2.2 Evaluating Determinants by Row Reduction
    3. 2.3 Properties of Determinants; Cramer's Rule
  7. CHAPTER 3 Euclidean Vector Spaces
    1. 3.1 Vectors in 2-Space, 3-Space, and n-Space
    2. 3.2 Norm, Dot Product, and Distance in Rn
    3. 3.3 Orthogonality
    4. 3.4 The Geometry of Linear Systems
    5. 3.5 Cross Product
  8. CHAPTER 4 General Vector Spaces
    1. 4.1 Real Vector Spaces
    2. 4.2 Subspaces
    3. 4.3 Linear Independence
    4. 4.4 Coordinates and Basis
    5. 4.5 Dimension
    6. 4.6 Change of Basis
    7. 4.7 Row Space, Column Space, and Null Space
    8. 4.8 Rank, Nullity, and the Fundamental Matrix Spaces
    9. 4.9 Basic Matrix Transformations in R2 and R3
    10. 4.10 Properties of Matrix Transformations
    11. 4.11 Geometry of Matrix Operators on R2
  9. CHAPTER 5 Eigenvalues and Eigenvectors
    1. 5.1 Eigenvalues and Eigenvectors
    2. 5.2 Diagonalization
    3. 5.3 Complex Vector Spaces
    4. 5.4 Differential Equations
    5. 5.5 Dynamical Systems and Markov Chains
  10. CHAPTER 6 Inner Product Spaces
    1. 6.1 Inner Products
    2. 6.2 Angle and Orthogonality in Inner Product Spaces
    3. 6.3 Gram–Schmidt Process; QR-Decomposition
    4. 6.4 Best Approximation; Least Squares
    5. 6.5 Mathematical Modeling Using Least Squares
    6. 6.6 Function Approximation; Fourier Series
  11. CHAPTER 7 Diagonalization and Quadratic Forms
    1. 7.1 Orthogonal Matrices
    2. 7.2 Orthogonal Diagonalization
    3. 7.3 Quadratic Forms
    4. 7.4 Optimization Using Quadratic Forms
    5. 7.5 Hermitian, Unitary, and Normal Matrices
  12. CHAPTER 8 Diagonalization and Quadratic Forms
    1. 8.1 General Linear Transformations
    2. 8.2 Compositions and Inverse Transformations
    3. 8.3 Isomorphism
    4. 8.4 Matrices for General Linear Transformations
    5. 8.5 Similarity
  13. CHAPTER 9 Numerical Methods
    1. 9.1 LU-Decompositions
    2. 9.2 The Power Method
    3. 9.3 Comparison of Procedures for Solving Linear Systems
    4. 9.4 Singular Value Decomposition
    5. 9.5 Data Compression Using Singular Value Decomposition
  14. CHAPTER 10 Diagonalization and Quadratic Forms
    1. 10.1 Constructing Curves and Surfaces Through Specified Points
    2. 10.2 The Earliest Applications of Linear Algebra
    3. 10.3 Cubic Spline Interpolation
    4. 10.4 Markov Chains
    5. 10.5 GraphTheory
    6. 10.6 Games of Strategy
    7. 10.7 Leontief Economic Models
    8. 10.8 Forest Management
    9. 10.9 Computer Graphics
    10. 10.10 EquilibriumTemperature Distributions
    11. 10.11 ComputedTomography
    12. 10.12 Fractals
    13. 10.13 Chaos
    14. 10.14 Cryptography
    15. 10.15 Genetics
    16. 10.16 Age-Specific Population Growth
    17. 10.17 Harvesting of Animal Populations
    18. 10.18 A Least Squares Model for Human Hearing
    19. 10.19 Warps and Morphs
    20. 10.20 Internet Search Engines
  15. APPENDIX A Working with Proofs
  16. APPENDIX B Complex Numbers
  17. Answers to Exercises
  18. Index
  19. APPLICATIONS AND HISTORICAL TOPICS
  20. End User License Agreement