Orthogonal representation of complex numbers

A.P. Yefremov1


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.


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