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MAT 04C Linear Algebra

Nguồn ngoài

MAT 04C Linear Algebra

Mathematics
Tác giả
Zoya Kravets
Nhà xuất bản
Mission College
Nguồn
LibreTexts
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 70 mục
  1. 01: Systems of Linear Equations
  2. 1.01: Systems of Linear Equations
  3. 1.02: Gaussian Elimination
  4. 1.03: Uniqueness of the Reduced Row-Echelon Form
  5. 1.04: Vectors
  6. 1.05: Vector Equations and Spans
  7. 1.06: Matrix Equations
  8. 1.07: Solution Sets
  9. 1.08: Applications of Linear Systems
  10. 1.09: Linear Independence
  11. 1.10: Exercises
  12. 02: Matrices
  13. 2.01: Matrix Arithmetic
  14. 2.02: Multiplication of Matrices
  15. 2.03: The ijth Entry of a Product
  16. 2.04: Properties of Matrix Multiplication
  17. 2.05: The Transpose
  18. 2.06: The Identity and Inverses
  19. 2.07: Finding the Inverse of a Matrix
  20. 2.08: Elementary Matrices
  21. 2.09: More on Matrix Inverses
  22. 2.10: LU Factorization
  23. 2.E: Exercises
  24. 03: Determinants
  25. 3.01: Basic Techniques
  26. 3.02: Properties of Determinants
  27. 3.03: Finding Determinants using Row Operations
  28. 3.04: Applications of the Determinant
  29. 3.E: Exercises
  30. 04: Linear Transformations
  31. 4.01: Linear Transformations
  32. 4.02: The Matrix of a Linear Transformation I
  33. 4.03: Properties of Linear Transformations. Invertible Linear Transformations.
  34. 4.04: Special Linear Transformations and Applications to Computer Graphics
  35. 4.05: One-to-One and Onto Transformations
  36. 4.06: Isomorphisms
  37. 4.07: The Kernel and Image of A Linear Map
  38. 4.08: The Matrix of a Linear Transformation II
  39. 4.09: The General Solution of a Linear System
  40. 4.E: Exercises
  41. 05: Vector Spaces and Subspaces
  42. 5.01: Vector Spaces
  43. 5.02: Subspaces
  44. 5.03: Basis and Dimension
  45. 5.04: Rank and Homogeneous Systems
  46. 5.05: The Rank Theorem
  47. 5.06: Bases as Coordinate Systems
  48. 5.07: Spanning Linear Independence and Basis in R
  49. 5.08: A Linear Transformations
  50. 5.09: A Isomorphisms
  51. 5.10: The Kernel and Image of a Linear Map
  52. 5.11: The Matrix of a Linear Transformation
  53. 5.E: Exercises
  54. 06: Eigenvalues and Eigenvectors
  55. 6.01: Eigenvalues and Eigenvectors
  56. 6.02: The Characteristic Polynomial
  57. 6.03: Diagonalization
  58. 6.04: Complex Eigenvalues
  59. 6.05: Stochastic Matrices
  60. 6.06: Similarity
  61. 07: Orthogonality
  62. 7.01: Dot Products and Orthogonality
  63. 7.02: Orthogonal Complements
  64. 7.03: Orthogonal Projection
  65. 7.04: Orthogonal Sets and Gram-Schmidt Process
  66. 7.05: The Method of Least Squares
  67. 7.06: Orthogonal Diagonalization
  68. 08: Some Prerequisite Topics
  69. 8.01: Sets and Set Notation
  70. 8.02: Well Ordering and Mathematical Induction