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Linear Algebra and Its Application

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Linear Algebra and Its Application

Mathematics
Author
Amira Alkeswani
Publisher
Cañada College
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 88 sections
  1. 01: Solving Systems of Linear Equations
  2. 1.01: Systems of Linear Equations
  3. 1.02: Matrix Notation and Row Reduction
  4. 1.03: Rank and Homogeneous Systems
  5. 1.04: Chemistry Reaction-Balancing Chemical Reaction
  6. 1.05: Applications to Physics and Resistor Networks
  7. 1.06: Chapters Exercises
  8. 02: Matrices
  9. 2.01: Matrix Addition Scalar Multiplication and Transposition
  10. 2.02: Matrix Multiplication
  11. 2.03: The Identity and Inverses
  12. 2.04: Finding the Inverse of a Matrix
  13. 2.05: Elementary Matrices
  14. 2.06: LU Factorization
  15. 03: Determinants
  16. 3.01: Basic Techniques
  17. 3.1E: Exercises for Section 3.1
  18. 3.02: Properties of Determinants
  19. 3.2E: Exercises for Section 3.2
  20. 3.03: Application of the Determinant to Inverses Cramer's Rule
  21. 3.3E: Exercises for Section 3.3
  22. 3.04: Determinants and Geometry
  23. 3.4E: Exercises for Section 3.4
  24. 04: Vector Spaces - R
  25. 4.01: Subspaces
  26. 4.02: Review of Vectors
  27. 4.2E: Exercises for Section 4.1
  28. 4.03: Dot and Cross Product
  29. 4.3E: Exercises for Section 4.2
  30. 4.04: Lines and Planes
  31. 4.4E: Exercises for Section 4.3
  32. 4.05: Spanning Sets in R
  33. 4.5.E: Exercise for Section 4.4
  34. 4.06: Linear Independence
  35. 4.6.E: Exercise for Section 4.5
  36. 4.07: Subspaces
  37. 4.08: Subspaces and Bases
  38. 4.8.E: Exercise for Section 4.6
  39. 4.09: Row Column and Null Spaces
  40. 4.9.E: Exercise for Section 4.7
  41. 4.10: Dot Products and Orthogonality
  42. 4.11: Orthogonal Vectors and Matrices
  43. 4.11.E: Exercise for Section 4.8
  44. 4.12: Gram-Schmidt Process
  45. 4.12.E: Exercises for Section 4.9
  46. 4.13: Orthogonal Complements
  47. 4.14: Orthogonal Projections
  48. 4.14.E: Exercise for Section 4.10
  49. 4.15: Orthogonal Projection
  50. 4.16: Least Squares Approximation
  51. 4.16.E: Exercises for Section 4.11
  52. 4.17: Vector Spaces and Subspace
  53. 4.18: Amira Vector Space Axioms
  54. 4.19: Amira Vector Subspace of R
  55. 4.20: The Real Vector Space Rn
  56. 4.E: Exercises
  57. 05: Linear Transformations
  58. 5.01: Prelude to Linear Transformations and Matrix Algebra
  59. 5.02: Linear Transformations
  60. 5.03: Matrix Transformations
  61. 5.04: One-to-one and Onto Transformations
  62. 5.05: The Invertible Matrix Theorem
  63. 06: Eigenvalues and Eigenvectors
  64. 6.01: An introduction to Eigenvalues and Eigenvectors
  65. 6.02: Finding eigenvalues and eigenvectors
  66. 6.03: Diagonalization similarity and powers of a matrix
  67. 6.04: Dynamical Systems
  68. 07: Honors Projects
  69. 7.01: Stochastic Matrices
  70. 7.02: An Application to Markov Chains
  71. 7.2.01: Absorbing Markov Chains
  72. 7.2.1.01: Absorbing Markov Chains (Exercises)
  73. 7.2.02: Introduction to Markov Chains
  74. 7.2.2.01: Introduction to Markov Chains (Exercises)
  75. 7.2.03: Regular Markov Chains
  76. 7.2.3.01: Regular Markov Chains (Exercises)
  77. 7.03: The Method of Least Squares
  78. 7.04: An Application to Linear Recurrences
  79. 7.4E: An Application to Linear Recurrences Exercises
  80. 7.05: An Application to Systems of Differential Equations
  81. 7.5E: An Application to Systems of Differential Equations Exercises
  82. 7.06: An Application to Computer Graphics
  83. 7.6E: An Application to Computer Graphics Exercises
  84. 7.07: An Application to Input-Output Economic Models
  85. 7.7E: An Application to Input-Output Economic Models Exercises
  86. 7.08: Markov chains and Google's PageRank algorithm
  87. 7.09: The Complex Number System
  88. 7.9.01: Solve Systems of Linear Equations with Complex Coefficients