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Linear Algebras

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Part of Cambridge Tracts in Mathematics

  • Date Published: March 2015
  • availability: Available
  • format: Paperback
  • isbn: 9781107493940

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  • Originally published in 1914 as number sixteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the theory of linear associative algebras. Textual notes are incorporated throughout. This book will be of value to anyone with an interest in algebra and the history of mathematics.

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    Product details

    • Date Published: March 2015
    • format: Paperback
    • isbn: 9781107493940
    • length: 82 pages
    • dimensions: 220 x 140 x 10 mm
    • weight: 0.12kg
    • availability: Available
  • Table of Contents

    Preface
    Part I. Definitions, Illustrations and Elementary Theorems:
    1-2. Ordinary complex numbers, number fields
    3-4. Matrices
    matric algebra as a linear algebra
    5. Definition of linear algebras, coordinates, units
    6-8. Division
    principal unit
    transformation of units
    9-10. Equations and polynomials in a single number
    11. Unique place of quaternions among algebras
    12-13. Properties of quaternions, relation to matrices
    14. Cayley's generalization of real quaternions
    15-17. Characteristic determinanats
    invariance
    18. Binary algebras
    19. Rank and rank equations of an algebra
    20. Ternary algebras with a modulus
    21-22. Reducibility, direct sum, direct product
    23-24. Units normalized relative to a number
    example
    Part II. Revision of Cartan's General Theory of Complex Linear Associative Algebras with a Modulus:
    25-27. Units having a character
    example
    28-34. Nilpotent numbers, normalized units
    examples
    35. Separation of algebras into two categories
    36-38. Algebras A1 of first category, nilpotent algebras
    39. Normalized units for A1
    40-45. Algebras A2 of the second category
    46. Any A2 has a quaternion sub-algebra
    47-48. Normalized units for A2
    determinant
    49. Invariant sub-algebra, simple algebras
    50-51. Main theorem
    commutative case
    Part III. Relations of Linear Algebras to Other Subjects:
    52. Linear associative algebras and linear groups
    53. Linear associative algebras and bilinear forms
    54. Relations of linear algebras and finite groups
    55. Dedekind's view for commutative associative algebras
    Part IV. Linear Algebras over a Field F:
    56. Statement of main theorem
    real simple algebras
    57. Algebras of Weierstrass
    58-60. Division algebras
    61. Statement of further results
    62. Analytic functions of hypercomplex numbers.

  • Author

    L. E. Dickson

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