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Linear Algebra (Math 3A UCI)

Nguồn ngoài

Linear Algebra (Math 3A UCI)

Mathematics
Tác giả
Kenn Huber
Nhà xuất bản
University of California Irvine
Nguồn
LibreTexts
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 103 mục
  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: Cramers 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: Dot Products and Orthogonal Complements
  76. 3.4.01: Dot Products and Orthogonality
  77. 3.4.02: Orthogonal Complements
  78. 3.4.03: Practice Set
  79. 3.05: Orthogonal Projection and Least Squares
  80. 3.5.01: Orthogonal Decomposition
  81. 3.5.02: Least Squares Solutions
  82. 3.5.03: Practice Set
  83. 3.06: Orthogonal Sets
  84. 3.6.01: Orthogonal Sets and Projection
  85. 3.6.02: Gram-Schmidt Process
  86. 3.6.03: Practice Set
  87. 04: Vector Spaces
  88. 4.01: General Vector Spaces and Subspaces
  89. 4.1.01: General Vector Spaces
  90. 4.1.02: Calculations in Vector Spaces
  91. 4.1.03: Practice Set
  92. 4.02: Linear Transformations in General Vector Spaces
  93. 4.2.01: Linear Transformations
  94. 4.2.02: Coordinatization
  95. 4.2.03: Practice Set
  96. 4.03: Examples and Applications
  97. 4.3.01: Differential Equations
  98. 4.3.02: Famous Transformations
  99. 4.3.03: Inner Product Spaces
  100. 4.3.04: Markov Chains
  101. 4.3.05: Page Rank
  102. 4.3.06: Quadratic Forms
  103. 4.3.07: Practice Set