Phu Xuan University Library
|
PXU E-LIB
Sign in
Math 26: Introduction to Linear Algebra

External

Math 26: Introduction to Linear Algebra

This textbook covers a standard first linear algebra course. Studies include vectors; vector spaces and subspaces; matrices; systems of linear equations; dimension; determinants; eigenvalues and eigenvectors; and linear transformations and their applications.

Mathematics
Author
Kenn Huber
Publisher
Irvine Valley College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 107 sections
  1. 01: Systems of Linear Equations
  2. 1.01: Systems of Linear Equations
  3. 1.1.01: Lines Planes and Space
  4. 1.1.02: Parametric Descriptions
  5. 1.1.03: Practice Set
  6. 1.02: Row Reduction
  7. 1.2.01: Elimination and Augmented Matrices
  8. 1.2.02: Echelon Forms
  9. 1.2.03: Free Variables
  10. 1.2.04: Practice Set
  11. 1.03: Vectors
  12. 1.3.01: Vector Algebra and Geometry
  13. 1.3.02: Vector Equations and Spans
  14. 1.3.03: Practice Set
  15. 1.04: Matrix Equations
  16. 1.4.01: Matrix Equations Spans and Consistency
  17. 1.4.02: Solutions to Matrix Equations
  18. 1.4.03: Practice Set
  19. 1.05: Linear Independence
  20. 1.5.01: Defining Linear Independence
  21. 1.5.02: Understanding Linear Independence
  22. 1.5.03: Practice Set
  23. 1.06: Subspaces
  24. 1.6.01: Defining Subspaces
  25. 1.6.02: Common Subspaces
  26. 1.6.03: Practice Set
  27. 1.07: Basis and Dimension
  28. 1.7.01: Defining Basis
  29. 1.7.02: Finding a Basis of a Subspace
  30. 1.7.03: Rank and Nullity
  31. 1.7.04: Practice Set
  32. 02: Linear Transformations and Matrix Algebra
  33. 2.01: Matrix Transformations
  34. 2.1.01: Matrices as Functions
  35. 2.1.02: Matrix Transformations
  36. 2.1.03: Practice Set
  37. 2.02: Linear Transformations
  38. 2.2.01: Linear Transformations
  39. 2.2.02: Matrix Representations
  40. 2.2.03: Practice Set
  41. 2.03: Matrix Algebra
  42. 2.3.01: Sums of Transformations and Matrices
  43. 2.3.02: Transformation Composition and Matrix Multiplication
  44. 2.3.03: Matrix Inverses
  45. 2.3.04: Practice Set
  46. 2.04: Invertibility
  47. 2.4.01: Invertibility of Linear Transformations
  48. 2.4.02: Invertibility of Matrices
  49. 2.4.03: Practice Set
  50. 2.05: Determinants- Definition
  51. 2.5.01: Definition of Determinant
  52. 2.5.02: Properties of the Determinant
  53. 2.5.03: Practice Set
  54. 2.06: Cofactor Expansions
  55. 2.6.01: Cofactor Expansion
  56. 2.6.02: Cramer's Rule and Adjugates
  57. 2.6.03: Practice Set
  58. 2.07: Determinants and Volumes
  59. 2.7.01: Determinants for Area and Volume
  60. 2.7.02: Practice Set
  61. 03: Vector Geometry
  62. 3.01: Change of Basis
  63. 3.1.01: Coordinatization
  64. 3.1.02: Similar Matrices
  65. 3.1.03: Practice Set
  66. 3.02: Eigenvalues and Eigenvectors
  67. 3.2.01: Eigenvalues and Eigenvectors Definitions
  68. 3.2.02: Eigenspaces
  69. 3.2.03: Characteristic Polynomial
  70. 3.2.04: Practice Set
  71. 3.03: Diagonalization and Geometry of Eigenvalues
  72. 3.3.01: Diagonalization
  73. 3.3.02: Geometry of Diagonalizable Matrices
  74. 3.3.03: Practice Set
  75. 3.04: Complex Eigenvalues
  76. 3.4.01: Complex Eigenvalues and Eigenvectors
  77. 3.4.02: Geometry of Matrices with Complex Eigenvalues
  78. 3.4.03: Practice Set
  79. 3.05: Dot Products and Orthogonal Complements
  80. 3.5.01: Dot Products and Orthogonality
  81. 3.5.02: Orthogonal Complements
  82. 3.5.03: Practice Set
  83. 3.06: Orthogonal Projection and Least Squares
  84. 3.6.01: Orthogonal Decomposition
  85. 3.6.02: Least Squares Solutions
  86. 3.6.03: Practice Set
  87. 3.07: Orthogonal Sets
  88. 3.7.01: Orthogonal Sets and Projection
  89. 3.7.02: Gram-Schmidt Process
  90. 3.7.03: Practice Set
  91. 04: Vector Spaces
  92. 4.01: General Vector Spaces and Subspaces
  93. 4.1.01: General Vector Spaces
  94. 4.1.02: Calculations in Vector Spaces
  95. 4.1.03: Practice Set
  96. 4.02: Linear Transformations in General Vector Spaces
  97. 4.2.01: Linear Transformations
  98. 4.2.02: Coordinatization
  99. 4.2.03: Practice Set
  100. 4.03: Examples and Applications
  101. 4.3.01: Differential Equations
  102. 4.3.02: Famous Transformations
  103. 4.3.03: Inner Product Spaces
  104. 4.3.04: Markov Chains
  105. 4.3.05: Page Rank
  106. 4.3.06: Practice Set
  107. 4.3.06: Quadratic Forms