Linear Algebra: A First Course

by Doli Bambhania, Fatemeh Yarahmadi and Bill Wilson

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This book offers a comprehensive and accessible introduction to linear algebra. It begins with methods for solving linear systems, followed by an exploration of matrices and their properties, including a dedicated chapter on determinants. The text then introduces vectors, covering essential concepts such as span, linear independence, subspaces, and linear transformations. From there, it develops spectral theory, including diagonalization and orthogonal diagonalization with their applications.

Description from LibreTexts.

Publisher
De Anza College
Subjects
Mathematics
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Program Page
  5. Table of Contents
  6. Licensing
  7. About the Book
  8. About the Authors
  9. 1: Systems of Equations
  10. 1.1: Systems of Linear Equations
  11. 1.1E: Exercises for Section 1.1
  12. 1.2: Gaussian Elimination
  13. 1.2E: Exercises for Section 1.2
  14. 1.3: Rank and Homogeneous Systems
  15. 1.3E: Exercises for Section 1.3
  16. 1.4: Balancing Chemical Reactions
  17. 1.4E: Exercises for Section 1.4
  18. 1.5: Applications to Physics
  19. 1.5E: Exercises for Section 1.5
  20. 1.6: Application to Polynomial Interpolation
  21. 1.6E: Exercises for Section 1.7
  22. 1.7: Gauss-Seidel Method
  23. 1.7E: Exercises for Section 1.8
  24. 2: Matrices
  25. 2.1: Matrix Operations
  26. 2.1E: Exercises for Section 2.1
  27. 2.2: The Inverse of a Matrix
  28. 2.2E: Exercises for Section 2.2
  29. 2.3: Elementary Matrices
  30. 2.3E: Exercises for Section 2.3
  31. 2.4: LU Factorization
  32. 2.4E: Exercises for Section 2.4
  33. 3: Determinants
  34. 3.1: Basic Techniques
  35. 3.1E: Exercises for Section 3.1
  36. 3.2: Properties of Determinants
  37. 3.2E: Exercises for Section 3.2
  38. 3.3: Application of the Determinant to Inverses; Cramer's Rule
  39. 3.3E: Exercises for Section 3.3
  40. 3.4: Determinants and Geometry
  41. 3.4E: Exercises for Section 3.4
  42. 4: Rⁿ
  43. 4.1: Review of Vectors
  44. 4.1E: Exercises for Section 4.1
  45. 4.2: Dot and Cross Product
  46. 4.2E: Exercises for Section 4.2
  47. 4.3: Lines and Planes
  48. 4.3E: Exercises for Section 4.3
  49. 4.4: Spanning Sets in Rⁿ
  50. 4.4.E: Exercise for Section 4.4
  51. 4.5: Linear Independence
  52. 4.5.E: Exercise for Section 4.5
  53. 4.6: Subspaces and Bases
  54. 4.6.E: Exercise for Section 4.6
  55. 4.7: Row, Column, and Null Spaces
  56. 4.7.E: Exercise for Section 4.7
  57. 4.8: Orthogonal Vectors and Matrices
  58. 4.8.E: Exercise for Section 4.8
  59. 4.9: Gram-Schmidt Process
  60. 4.9.E: Exercises for Section 4.9
  61. 4.10: Orthogonal Projections
  62. 4.10.E: Exercise for Section 4.10
  63. 4.11: Least Squares Approximation
  64. 4.11.E: Exercises for Section 4.11
  65. 5: Linear Transformations
  66. 5.1: Linear Transformations
  67. 5.1E: Exercises for Section 5.1
  68. 5.2: The Matrix of a Linear Transformation I
  69. 5.2E: Exercises for Section 5.2
  70. 5.3: Properties of Linear Transformations
  71. 5.3E: Exercises for Section 5.3
  72. 5.4: Special Linear Transformations in Two and Three Dimensions
  73. 5.4E: Exercises for Section 5.4
  74. 5.5: One-to-One and Onto Transformations
  75. 5.5E: Exercises for Section 5.5
  76. 5.6: Isomorphisms
  77. 5.6E: Exercises for Section 5.6
  78. 5.7: The Kernel and Image of A Linear Map
  79. 5.7E: Exercises for Section 5.7
  80. 5.8: The Matrix of a Linear Transformation II
  81. 5.8E: Exercises for Section 5.8
  82. 5.9: The General Solution of a Linear System
  83. 5.9E: Exercises for Section 5.9
  84. 6: Spectral Theory
  85. 6.1: Eigenvalues and Eigenvectors of a Matrix
  86. 6.1E: Exercises for Section 6.1
  87. 6.2: Eigenvalues and Eigenvectors for Special Matrices
  88. 6.2E: Exercises for Section 6.2
  89. 6.3: Diagonalization
  90. 6.3E: Exercises for Section 6.3
  91. 6.4: Applications of Spectral Theory
  92. 6.4E: Exercises for Section 6.4
  93. 6.5: Markov Matrices
  94. 6.5E: Exercises for Section 6.5
  95. 6.6: Dynamical Systems
  96. 6.6E: Exercises for Section 6.6
  97. 6.7: Orthogonal Diagonalization
  98. 6.7E: Exercises for Section 6.7
  99. 6.8: Singular Value Decomposition
  100. 6.8E: Exercises for Section 6.8
  101. 6.9: Special Factorizations
  102. 6.9E: Exercises for Section 6.9
  103. 6.10: Quadratic Forms
  104. 6.10E: Exercises for Section 6.10
  105. 7: Vector Spaces
  106. 7.1: Vector Space - Definition
  107. 7.1.E: Exercises for Section 7.1
  108. 7.2: Vector Space - Examples
  109. 7.2.E: Exercises for Section 7.2
  110. 7.3: Spanning Sets
  111. 7.3E: Exercises for Section 7.3
  112. 7.4: Linear Independence
  113. 7.4E: Exercises for Section 7.4
  114. 7.5: Subspaces
  115. 7.5E: Exercises for Section 7.5
  116. 7.6: Basis
  117. 7.6.E: Exercises for Section 7.6
  118. 7.7: Sums and Intersections
  119. 7.7E: Exercises for Section 7.7
  120. 7.8: Linear Transformations
  121. 7.8E: Exercises for Section 7.8
  122. 7.9: Isomorphisms
  123. 7.9E: Exercises for Section 7.9
  124. 7.10: The Kernel and Image of a Linear Map
  125. 7.10E: Exercises for Section 7.10
  126. 7.11: The Matrix of a Linear Transformation
  127. 7.11E: Exercises for Section 7.11
  128. 7.12: Inner Product Spaces
  129. 7.12E: Exercises for Section 7.12
  130. 8: Appendices
  131. 8.1: Sets and Set Notation
  132. 8.2: Well Ordering and Induction
  133. Back Matter
  134. Index
  135. Detailed Licensing
  136. Glossary
  137. Detailed Licensing