A First Course in Linear Algebra

by Ken Kuttler

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The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced.

Description from LibreTexts.

Publisher
Brigham Young University
Subjects
Mathematics, Linear Algebra
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. About the Book
  6. Licensing
  7. 1: Systems of Equations
  8. 1.1: Systems of Equations, Geometry
  9. 1.2: Systems of Equations, Algebraic Procedures
  10. 1.3: Gaussian Elimination
  11. 1.4: Uniqueness of the Reduced Row-Echelon Form
  12. 1.5: Rank and Homogeneous Systems
  13. 1.6: Balancing Chemical Reactions
  14. 1.7: Dimensionless Variables
  15. 1.8: An Application to Resistor Networks
  16. 1.9: Exercises
  17. 2: Matrices
  18. 2.1: Matrix Arithmetic
  19. 2.2: Multiplication of Matrices
  20. 2.3: The ijth Entry of a Product
  21. 2.4: Properties of Matrix Multiplication
  22. 2.5: The Transpose
  23. 2.6: The Identity and Inverses
  24. 2.7: Finding the Inverse of a Matrix
  25. 2.8: Elementary Matrices
  26. 2.9: More on Matrix Inverses
  27. 2.10: LU Factorization
  28. 2.E: Exercises
  29. 3: Determinants
  30. 3.1: Basic Techniques
  31. 3.2: Properties of Determinants
  32. 3.3: Finding Determinants using Row Operations
  33. 3.4: Applications of the Determinant
  34. 3.E: Exercises
  35. 4: Rⁿ
  36. 4.1: Vectors in Rⁿ
  37. 4.2: Vector Algebra
  38. 4.3: Geometric Meaning of Vector Addition
  39. 4.4: Length of a Vector
  40. 4.5: Geometric Meaning of Scalar Multiplication
  41. 4.6: Parametric Lines
  42. 4.7: The Dot Product
  43. 4.8: Planes in Rⁿ
  44. 4.9: The Cross Product
  45. 4.10: Spanning, Linear Independence and Basis in Rⁿ
  46. 4.11: Orthogonality
  47. 4.12: Applications
  48. 4.E: Exercises
  49. 5: Linear Transformations
  50. 5.1: Linear Transformations
  51. 5.2: The Matrix of a Linear Transformation I
  52. 5.3: Properties of Linear Transformations
  53. 5.4: Special Linear Transformations in R²
  54. 5.5: One-to-One and Onto Transformations
  55. 5.6: Isomorphisms
  56. 5.7: The Kernel and Image of A Linear Map
  57. 5.8: The Matrix of a Linear Transformation II
  58. 5.9: The General Solution of a Linear System
  59. 5.E: Exercises
  60. 6: Complex Numbers
  61. 6.1: Complex Numbers
  62. 6.2: Polar Form
  63. 6.3: Roots of Complex Numbers
  64. 6.4: The Quadratic Formula
  65. 6.E: Exercises
  66. 7: Spectral Theory
  67. 7.1: Eigenvalues and Eigenvectors of a Matrix
  68. 7.2: Diagonalization
  69. 7.3: Applications of Spectral Theory
  70. 7.4: Orthogonality
  71. 7.E: Exercises
  72. 8: Some Curvilinear Coordinate Systems
  73. 8.1: Polar Coordinates and Polar Graphs
  74. 8.2: Spherical and Cylindrical Coordinates
  75. 8.E: Exercises
  76. 9: Vector Spaces
  77. 9.1: Algebraic Considerations
  78. 9.2: Spanning Sets
  79. 9.3: Linear Independence
  80. 9.4: Subspaces and Basis
  81. 9.5: Sums and Intersections
  82. 9.6: Linear Transformations
  83. 9.7: Isomorphisms
  84. 9.8: The Kernel and Image of a Linear Map
  85. 9.9: The Matrix of a Linear Transformation
  86. 9.E: Exercises
  87. 10: Some Prerequisite Topics
  88. 10.1: Sets and Set Notation
  89. 10.2: Well Ordering and Induction
  90. Back Matter
  91. Index
  92. Detailed Licensing