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