Gravitation and Cosmology

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

Orthogonal representation of complex numbers

  • A. P. Yefremov


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.


Complex Number Imaginary Unit Diagonal Operator Vector Description Orthogonal Representation 
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  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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