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Linear Algebra (MTH 288)

Nguồn ngoài

Linear Algebra (MTH 288)

This textbook is adapted from the book "Linear Algebra with Applications" by W. Keith Nicholson. The topics have been re-ordered to align with MTH 288: Linear Algebra as taught at Cleveland State University. Optional topics have been moved to either Chapter 7: Applications, or the Appendix.

Mathematics
Tác giả
Sara Froehlich & Todd Romutis
Nhà xuất bản
Cleveland State University
Nguồn
LibreTexts
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 166 mục
  1. 01: Systems of Linear Equations
  2. 1.01: Prelude to Systems of Linear Equations
  3. 1.02: Solutions and Elementary Operations
  4. 1.2E: Exercises for Section 1.1
  5. 1.03: Gaussian Elimination
  6. 1.3E: Solutions and Elementary Operations Exercises
  7. 1.04: Homogeneous Equations
  8. 1.4E: Homogeneous Equations
  9. 1.E: Supplementary Exercises for Chapter 1
  10. 02: Matrix Algebra
  11. 2.01: Prelude to Matrix Algebra
  12. 2.02: Matrix Addition Scalar Multiplication and Transposition
  13. 2.2E: Matrix Addition Scalar Multiplication and Transposition Exercises
  14. 2.03: Equations Matricies and Transformations
  15. 2.3E: Matrix-Vector Multiplication Exercises
  16. 2.04: Matrix Multiplication
  17. 2.4E: Matrix Multiplication Exercises
  18. 2.05: Matrix Inverses
  19. 2.5E: Matrix Inverses Exercises
  20. 2.06: Elementary Matrices
  21. 2.6E: Elementary Matrices Exercises
  22. 2.07: Linear Transformations
  23. 2.7E: Linear Transformations Exercises
  24. 2.E: Supplementary Exercises for Chapter 2
  25. 03: Determinants and Diagonalization
  26. 3.01: Prelude to Determinants and Diagonalization
  27. 3.02: The Cofactor Expansion
  28. 3.2E: The Cofactor Expansion Exercises
  29. 3.03: Determinants and Matrix Inverses
  30. 3.3E: Determinants and Matrix Inverses Exercises
  31. 3.04: Eigenvalues and Eigenvectors
  32. 3.4E: Eigenvalues and Eigenvectors Exercises
  33. 3.05: Diagonalization
  34. 3.5E: Diagonalization Exercises
  35. 3.E: Supplementary Exercises for Chapter 3
  36. 04: Vector Geometry
  37. 4.01: Prelude to Vector Geometry
  38. 4.02: Vectors and Lines
  39. 4.2E: Vectors and Lines Exercises
  40. 4.03: Projections and Planes
  41. 4.3E: Projections and Planes Exercises
  42. 4.04: More on the Cross Product
  43. 4.4E: More on the Cross Product Exercises
  44. 4.05: Linear Operators on R
  45. 4.5E: Linear Operators on R Exercises
  46. 4.E: Supplementary Exercises for Chapter 4
  47. 05: Vector Space R
  48. 5.01: Prelude to Vector Space R
  49. 5.02: Subspaces and Spanning
  50. 5.2E: Subspaces and Spanning Exercises
  51. 5.03: Independence and Dimension
  52. 5.3E: Independence and Dimension Exercises
  53. 5.04: Rank of a Matrix
  54. 5.4E: Rank of a Matrix Exercises
  55. 5.05: Similarity and Diagonalization
  56. 5.5E: Similarity and Diagonalization Exercises
  57. 5.06: Orthogonality
  58. 5.6E: Orthogonality Exercises
  59. 5.07: Orthogonal Complements and Projections
  60. 5.7.01: Orthogonal Complements and Projections Exercises
  61. 5.08: Best Approximation and Least Squares
  62. 5.8E: Best Approximation and Least Squares Exercises
  63. 5.E: Supplementary Exercises for Chapter 5
  64. 06: Vector Spaces
  65. 6.01: Prelude to Vector Spaces
  66. 6.02: Examples and Basic Properties
  67. 6.2E: Examples and Basic Properties Exercises
  68. 6.03: Subspaces and Spanning Sets
  69. 6.3E: Subspaces and Spanning Sets Exercises
  70. 6.04: Linear Independence and Dimension
  71. 6.4E: Linear Independence and Dimension Exercises
  72. 6.05: Finite Dimensional Spaces
  73. 6.5E: Finite Dimensional Spaces Exercises
  74. 6.06: An Application to Polynomials
  75. 6.6E: An Application to Polynomials Exercises
  76. 6.07: Linear Transformations of Vector Spaces
  77. 6.7E: Examples and Elementary Properties Exercises
  78. 6.08: Kernel and Image of a Linear Transformation
  79. 6.8E: Kernel and Image of a Linear Transformation Exercises
  80. 6.E: Supplementary Exercises for Chapter 6
  81. 07: Applications
  82. 7.01: An Application to Electrical Networks
  83. 7.1.01: An Application to Electrical Networks Exercises
  84. 7.02: An Application to Input-Output Economic Models
  85. 7.2.01: An Application to Input-Output Economic Models Exercises
  86. 7.03: An Application to Markov Chains
  87. 7.3E: An Application to Markov Chains Exercises
  88. 7.04: An Application to Network Flow
  89. 7.4.01: An Application to Network Flow Exercises
  90. 7.05: An Application to Chemical Reactions
  91. 7.5.01: An Application to Chemical Reactions Exercises
  92. 7.06: An Application to Computer Graphics
  93. 7.6E: An Application to Computer Graphics Exercises
  94. 7.07: An Application to Linear Recurrences
  95. 7.7E: An Application to Linear Recurrences Exercises
  96. 7.08: An Application to Systems of Differential Equations
  97. 7.8E: An Application to Systems of Differential Equations Exercises
  98. 7.09: Linear Dynamical Systems
  99. 7.9E: Linear Dynamical Systems Exercises
  100. 7.10: An Application to Correlation and Variance
  101. 7.10.01: An Application to Correlation and Variance Exercises
  102. 7.11: An Application to Differential Equations
  103. 7.11E: An Application to Differential Equations Exercises
  104. 08: Appendices
  105. 8.A: Complex Numbers
  106. 1.01: Exercises for Complex Numbers
  107. 8.B: Proofs
  108. 1.01: Exercises for Proofs
  109. 8.C: Mathematical Induction
  110. 1.01: Exercises for Mathematical Induction
  111. 8.D: Polynomials
  112. 8.E: LU-Factorization
  113. 1.01: LU-Factorization Exercises
  114. 8.F: Proof of the Cofactor Expansion Theorem
  115. 1.01: Proof of the Cofactor Expansion Theorem Exercises
  116. 8.G: Isomorphisms and Composition
  117. 1.01: Isomorphisms and Composition Exercises
  118. 8.H: A Theorem about Differential Equations
  119. 8.I: More on Linear Recurrences
  120. 1.01: Exercises for Linear Recurrences
  121. 8.J: Orthogonality
  122. 1.01: Prelude to Orthogonality
  123. 1.02: Orthogonal Diagonalization
  124. 1.2E: Orthogonal Diagonalization Exercises
  125. 1.03: Positive Definite Matrices
  126. 1.3E: Positive Definite Matrices Exercises
  127. 1.04: QR-Factorization
  128. 1.4E: QR-Factorization Exercises
  129. 1.05: Computing Eigenvalues
  130. 1.5E: Computing Eigenvalues Exercises
  131. 1.06: The Singular Value Decomposition
  132. 1.6E: The Singular Value Decomposition Exercises
  133. 1.07: Complex Matrices
  134. 1.7E: Complex Matrices Exercises
  135. 1.08: An Application to Linear Codes over Finite Fields
  136. 1.8E: An Application to Linear Codes over Finite Fields Exercises
  137. 1.09: An Application to Quadratic Forms
  138. 1.9E: An Application to Quadratic Forms Exercises
  139. 1.10: An Application to Constrained Optimization
  140. 1.11: An Application to Statistical Principal Component Analysis
  141. 8.K: Change of Basis
  142. 1.01: Prelude to Change of Basis
  143. 1.02: The Matrix of a Linear Transformation
  144. 1.2E: The Matrix of a Linear Transformation Exercises
  145. 1.03: Operators and Similarity
  146. 1.3E: Operators and Similarity Exercises
  147. 1.04: Invariant Subspaces and Direct Sums
  148. 1.4E: Invariant Subspaces and Direct Sums Exercises
  149. 8.L: Canonical Forms
  150. 1.01: Prelude to Canonical Forms
  151. 1.02: Block Triangular Form
  152. 1.2E: Block Triangular Form Exercises
  153. 1.03: The Jordan Canonical Form
  154. 1.3E: The Jordan Canonical Form Exercises
  155. 8.M: Inner Product Spaces
  156. 1.01: Prelude to Inner Product Spaces
  157. 1.02: Inner Products and Norms
  158. 1.2E: Inner Products and Norms Exercises
  159. 1.03: Orthogonal Sets of Vectors
  160. 1.3E: Orthogonal Sets of Vectors Exercises
  161. 1.04: Orthogonal Diagonalization
  162. 1.4E: Orthogonal Diagonalization Exercises
  163. 1.05: Isometries
  164. 1.5E: Isometries Exercises
  165. 1.06: An Application to Fourier Approximation
  166. 1.6E: An Application to Fourier Approximation Exercises