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Linear Algebra

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Linear Algebra

Linear Algebra is the branch of mathematics aimed at solving systems of linear equations with a finite number of unknowns.

Linear AlgebraMathematics
Author
Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling
Publisher
University of California, Davis
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 77 sections
  1. 01: What is linear algebra
  2. 1.E: Exercises for Chapter 1
  3. 02: Introduction to Complex Numbers
  4. 2.01: Definition of Complex Numbers
  5. 2.02: Operations on complex numbers
  6. 2.03: Polar Form and Geometric Interpretation
  7. 2.E: Exercises for Chapter 2
  8. 03: 3. The fundamental theorem of algebra and factoring polynomials
  9. 3.01: The Fundamental Theorem of Algebra
  10. 3.02: Factoring polynomials
  11. 3.E: Exercises for Chapter 3
  12. 04: Vector spaces
  13. 4.01: Definition of vector spaces
  14. 4.02: Elementary properties of vector spaces
  15. 4.03: Subspaces
  16. 4.04: Sums and direct sum
  17. 4.E: Exercises for Chapter 4
  18. 05: Span and Bases
  19. 5.01: Linear Span
  20. 5.02: Linear Independence
  21. 5.03: Bases
  22. 5.04: Dimension
  23. 5.E: Exercises for Chapter 5
  24. 06: Linear Maps
  25. 6.01: Denition and elementary properties
  26. 6.02: Null spaces
  27. 6.03: Ranges
  28. 6.04: Homomorphisms
  29. 6.05: The dimension formula
  30. 6.06: The matrix of a linear map
  31. 6.07: Invertibility
  32. 6.E: Exercises for Chapter 6
  33. 07: Eigenvalues and Eigenvectors
  34. 7.01: Invariant Subspaces
  35. 7.02: Eigenvalues
  36. 7.03: Diagonal matrices
  37. 7.04: Existence of Eigenvalues
  38. 7.05: Upper Triangular Matrices
  39. 7.06: Diagonalization of (2times 2) matrices and Applications
  40. 7.E: Exercises for Chapter 7
  41. 08: Permutations and the Determinant
  42. 8.01: Permutations
  43. 8.02: Determinants
  44. 8.E: Exercises for Chapter 8
  45. 09: Inner product spaces
  46. 9.01: Inner Products
  47. 9.02: Norms
  48. 9.03: Orthogonality
  49. 9.04: Orthonormal bases
  50. 9.05: The Gram-Schmidt Orthogonalization procedure
  51. 9.06: Orthogonal projections and minimization problems
  52. 9.E: Exercises for Chapter 9
  53. 10: Change of bases
  54. 10.01: Coordinate Vectors
  55. 10.02: 10.2 Change of basis transformation
  56. 10.E: Exercises for Chapter 10
  57. 11: The Spectral Theorem for normal linear maps
  58. 11.01: Self-adjoint or hermitian operators
  59. 11.02: Normal operators
  60. 11.03: Normal operators and the spectral decomposition
  61. 11.04: Diagonalization
  62. 11.05: Positive operators
  63. 11.06: Polar decomposition
  64. 11.07: Singular-value decomposition
  65. 11.E: Exercises for Chapter 11
  66. 12: Supplementary notes on matrices and linear systems
  67. 12.01: From linear systems to matrix equations
  68. 12.02: Matrix arithmetic
  69. 12.03: Solving linear systems by factoring the coefficient matrix
  70. 12.04: Matrices and linear maps
  71. 12.05: Special operations on matrices
  72. 12.E: Exercises
  73. 13: Appendices
  74. 13.01: The Language of Sets and Functions
  75. 13.02: Summary of Algebraic Structures
  76. 13.03: Some Common Mathematical Symbols and Abbreviations
  77. 13.04: Summary of Notation Used