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Linear Algebra (MTH 288)

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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
Author
Sara Froehlich & Todd Romutis
Publisher
Cleveland State University
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 166 sections
  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