Orthogonal representation of complex numbers

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...

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Bibliographic Details
Published inGravitation & cosmology Vol. 16; no. 2; pp. 137 - 139
Main Author Yefremov, A. P.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.04.2010
Subjects
Astronomy
Astrophysics and Astroparticles
Classical and Quantum Gravitation
Observations and Techniques
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Diagonal Operator
Complex Number
Imaginary Unit
Orthogonal Representation
Vector Description
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Summary: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.
ISSN:0202-2893
1995-0721
DOI:10.1134/S0202289310020064