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Gravitation and Cosmology

, Volume 16, Issue 2, pp 137–139 | Cite as

Orthogonal representation of complex numbers

  • A. P. Yefremov
Article

Abstract

Units of the complex numbers algebra given by 2 × 2 matrices are shown to be composed of elementary spinors. This leads to a novel representation of any complex number in a two-dimensional orthogonal form, each direction referred to an idempotent matrix built of the spinors’ components. Introduction of a “diagonal operator,” a poly-index generalization of the Kronecker symbol, allows establishing equivalence of idempotent matrices and a vector description of the orthogonal axes.

Keywords

Complex Number Imaginary Unit Diagonal Operator Vector Description Orthogonal Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. P. Yefremov, arXiv: math-ph/0501055.Google Scholar
  2. 2.
    V. V. Kisil, arXiv: 0707.4024.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. P. Yefremov
    • 1
  1. 1.Institute of Gravitation and CosmologyPeoples’ Friendship University of RussiaMoscowRussia

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