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A First Course in Linear Algebra

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A First Course in Linear Algebra

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.

Mathematics
Author
Ken Kuttler
Publisher
Brigham Young University
Source
LibreTexts
License
CC BY
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 83 sections
  1. 01: Systems of Equations
  2. 1.01: Systems of Equations Geometry
  3. 1.02: Systems of Equations Algebraic Procedures
  4. 1.03: Gaussian Elimination
  5. 1.04: Uniqueness of the Reduced Row-Echelon Form
  6. 1.05: Rank and Homogeneous Systems
  7. 1.06: Balancing Chemical Reactions
  8. 1.07: Dimensionless Variables
  9. 1.08: An Application to Resistor Networks
  10. 1.09: Exercises
  11. 02: Matrices
  12. 2.01: Matrix Arithmetic
  13. 2.02: Multiplication of Matrices
  14. 2.03: The ijth Entry of a Product
  15. 2.04: Properties of Matrix Multiplication
  16. 2.05: The Transpose
  17. 2.06: The Identity and Inverses
  18. 2.07: Finding the Inverse of a Matrix
  19. 2.08: Elementary Matrices
  20. 2.09: More on Matrix Inverses
  21. 2.10: LU
  22. 2.E: Exercises
  23. 03: Determinants
  24. 3.01: Basic Techniques
  25. 3.02: Properties of Determinants
  26. 3.03: Finding Determinants using Row Operations
  27. 3.04: Applications of the Determinant
  28. 3.E: Exercises
  29. 04: R
  30. 4.01: Vectors in R
  31. 4.02: Vector Algebra
  32. 4.03: Geometric Meaning of Vector Addition
  33. 4.04: Length of a Vector
  34. 4.05: Geometric Meaning of Scalar Multiplication
  35. 4.06: Parametric Lines
  36. 4.07: The Dot Product
  37. 4.08: Planes in R
  38. 4.09: The Cross Product
  39. 4.10: Spanning Linear Independence and Basis in R
  40. 4.11: Orthogonality
  41. 4.12: Applications
  42. 4.E: Exercises
  43. 05: Linear Transformations
  44. 5.01: Linear Transformations
  45. 5.02: The Matrix of a Linear Transformation I
  46. 5.03: Properties of Linear Transformations
  47. 5.04: Special Linear Transformations in R
  48. 5.05: One-to-One and Onto Transformations
  49. 5.06: Isomorphisms
  50. 5.07: The Kernel and Image of A Linear Map
  51. 5.08: The Matrix of a Linear Transformation II
  52. 5.09: The General Solution of a Linear System
  53. 5.E: Exercises
  54. 06: Complex Numbers
  55. 6.01: Complex Numbers
  56. 6.02: Polar Form
  57. 6.03: Roots of Complex Numbers
  58. 6.04: The Quadratic Formula
  59. 6.E: Exercises
  60. 07: Spectral Theory
  61. 7.01: Eigenvalues and Eigenvectors of a Matrix
  62. 7.02: Diagonalization
  63. 7.03: Applications of Spectral Theory
  64. 7.04: Orthogonality
  65. 7.E: Exercises
  66. 08: Some Curvilinear Coordinate Systems
  67. 8.01: Polar Coordinates and Polar Graphs
  68. 8.02: Spherical and Cylindrical Coordinates
  69. 8.E: Exercises
  70. 09: Vector Spaces
  71. 9.01: Algebraic Considerations
  72. 9.02: Spanning Sets
  73. 9.03: Linear Independence
  74. 9.04: Subspaces and Basis
  75. 9.05: Sums and Intersections
  76. 9.06: Linear Transformations
  77. 9.07: Isomorphisms
  78. 9.08: The Kernel and Image of a Linear Map
  79. 9.09: The Matrix of a Linear Transformation
  80. 9.E: Exercises
  81. 10: Some Prerequisite Topics
  82. 10.01: Sets and Set Notation
  83. 10.02: Well Ordering and Induction