Linear Algebra Problem Book /

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Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebra ;and nowadays that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Halmos, Paul R.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2013.
Colección:Dolciani mathematical expositions.
Temas:
Algebras, Linear.
Algebras, Linear > Problems, exercises, etc.
Algèbre linéaire.
Algèbre linéaire > Problèmes et exercices.
Algebras, Linear
Problems and exercises
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Linear Algebra Problem Book
  • copyright page
  • Preface
  • Contents
  • 1 SCALARS
  • 1. Double addition
  • 2. Half double addition
  • 3. Exponentiation
  • 4. Complex numbers
  • 5. Affine transformations
  • 6. Matrix multiplication
  • 7. Modular multiplication
  • 8. Small operations
  • 9. Identity elements
  • 10. Complex inverses
  • 11. Affine inverses
  • 12. Matrix inverses
  • 13. Abelian groups
  • 14. Groups
  • 15. Independent group axioms
  • 16. Fields
  • 17. Addition and multiplication in fields
  • 18. Distributive failure
  • 19. Finite fields2 VECTORS
  • 20. Vector spaces
  • 21. Examples
  • 22. Linear combinations
  • 23. Subspaces
  • 24. Unions of subspaces
  • 25. Spans
  • 26. Equalities of spans
  • 27. Some special spans
  • 28. Sums of subspaces
  • 29. Distributive subspaces
  • 30. Total sets
  • 31. Dependence
  • 32. Independence
  • 3 BASES
  • 33. Exchanging bases
  • 34. Simultaneous complements
  • 35. Examples of independence
  • 36. Independence over R and Q
  • 37. Independence in C^2
  • 38. Vectors common to different bases
  • 39. Bases in C^3
  • 40. Maximal independent sets41. Complex as real
  • 42. Subspaces of full dimension
  • 43. Extended bases
  • 44. Finite-dimensional subspaces
  • 45. Minimal total sets
  • 46. Existence of minimal total sets
  • 47. Infinitely total sets
  • 48. Relatively independent sets
  • 49. Number of bases in a finite vector space
  • 50. Direct sums
  • 51. Quotient spaces
  • 52. Dimension of a quotient space
  • 53. Additivity of dimension
  • 4 TRANSFORMATIONS
  • 54. Linear transformations
  • 55. Domain and range
  • 56. Kernel
  • 57. Composition
  • 58. Range inclusion and factorization59. Transformations as vectors
  • 60. Invertibility
  • 61. Invertibility examples
  • 62. Determinants: 2Ã? 2
  • 63. Determinants: n Ã?n
  • 64. Zero-one matrices
  • 65. Invertible matrix bases
  • 66. Finite-dimensional invertibility
  • 67. Matrices
  • 68. Diagonal matrices
  • 69. Universal commutativity
  • 70. Invariance
  • 71. Invariant complements
  • 72. Projections
  • 73. Sums of projections
  • 74. Not quite idempotence
  • 5 DUALITY
  • 75. Linear functionals
  • 76. Dual spaces
  • 77. Solution of equations
  • 78. Reflexivity79. Annihilators
  • 80. Double annihilators
  • 81. Adjoints
  • 82. Adjoints of projections
  • 83. Matrices of adjoints
  • 6 SIMILARITY
  • 84. Change of basis: vectors
  • 85. Change of basis: coordinates
  • 86. Similarity: transformations
  • 87. Similarity: matrices
  • 88. Inherited similarity
  • 89. Similarity: real and complex
  • 90. Rank and nullity
  • 91. Similarity and rank
  • 92. Similarity of transposes
  • 93. Ranks of sums
  • 94. Ranks of products
  • 95. Nullities of sums and products
  • 96. Some similarities

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