Table of Contents

  1. A First Course in Linear Algebra
  2. Copyright
  3. Author Biography
  4. Edition
  5. Publisher
  6. Table of Contents
  7. Dedication
  8. Chapter 1. Theorems
  9. Chapter 2. Notation
  10. Chapter 3. Diagrams
  11. Chapter 4. Examples
  12. Preface
  13. Acknowledgements
  14. Part I. Part C  Core
    1. Chapter 1. Chapter SLE  Systems of Linear Equations
      1. Section WILA  What is Linear Algebra?
      2. Section SSLE  Solving Systems of Linear Equations
      3. Section RREF  Reduced Row-Echelon Form
      4. Section HSE  Homogeneous Systems of Equations
      5. Section NM  Nonsingular Matrices
    2. Chapter 2. Chapter V  Vectors
      1. Section SS  Spanning Sets
      2. Section O  Orthogonality
    3. Chapter 3. Chapter M  Matrices
      1. Section MM  Matrix Multiplication
      2. Section MISLE  Matrix Inverses and Systems of Linear Equations
      3. Section MINM  Matrix Inverses and Nonsingular Matrices
      4. Section CRS  Column and Row Spaces
    4. Chapter 4. Chapter VS  Vector Spaces
    5. Chapter 5. Chapter D  Determinants
      1. Section PDM  Properties of Determinants of Matrices
    6. Chapter 6. Chapter E  Eigenvalues
      1. Section PEE  Properties of Eigenvalues and Eigenvectors
    7. Chapter 7. Chapter LT  Linear Transformations
      1. Section ILT  Injective Linear Transformations
      2. Section SLT  Surjective Linear Transformations
      3. Section IVLT  Invertible Linear Transformations
    8. Chapter 8. Chapter R  Representations
      1. Section CB  Change of Basis
      2. Section OD  Orthonormal Diagonalization
      3. Section NLT  Nilpotent Linear Transformations
      4. Section IS  Invariant Subspaces
      5. Section JCF  Jordan Canonical Form
    9. Chapter 9. Appendix CN  Computation Notes
      1. Section MMA  Mathematica
      2. Section TI86  Texas Instruments 86
      3. Section TI83  Texas Instruments 83
      4. Section SAGE  SAGE: Open Source Mathematics Software
    10. Chapter 10. Appendix P  Preliminaries
      1. Section CNO  Complex Number Operations
      2. Section SET  Sets
      3. Section PT  Proof Techniques
    11. Chapter 11. Appendix A  Archetypes
      1. Archetype A
      2. Archetype B
      3. Archetype C
      4. Archetype D
      5. Archetype E
      6. Archetype F
      7. Archetype G
      8. Archetype H
      9. Archetype I
      10. Archetype J
      11. Archetype K
      12. Archetype L
      13. Archetype M
      14. Archetype N
      15. Archetype O
      16. Archetype P
      17. Archetype Q
      18. Archetype R
      19. Archetype S
      20. Archetype T
      21. Archetype U
      22. Archetype V
      23. Archetype W
      24. Archetype X
    12. Chapter 12. Appendix GFDL  GNU Free Documentation License
  15. Part II. Part T  Topics
    1. Chapter 14. Section T  Trace
    2. Chapter 15. Section HP  Hadamard Product
    3. Chapter 16. Section VM  Vandermonde Matrix
    4. Chapter 17. Section PSM  Positive Semi-definite Matrices
    5. Chapter 18. Chapter MD  Matrix Decompositions
      1. Section ROD  Rank One Decomposition
      2. Section TD  Triangular Decomposition
      3. Section SVD  Singular Value Decomposition
      4. Section SR  Square Roots
      5. Section POD  Polar Decomposition
  16. Part III. Part A  Applications
    1. Chapter 19. Section CF  Curve Fitting
    2. Chapter 20. Section SAS  Sharing A Secret
    3. Chapter 21. Contributors
    4. Chapter 22. Definitions
  1. Part I. Part C  Core