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On the Structure of SO(3): Trace and Canonical Decompositions

Author

Listed:
  • Demeter Krupka

    (Lepage Research Institute, 08001 Prešov, Slovakia)

  • Ján Brajerčík

    (Lepage Research Institute, 08001 Prešov, Slovakia
    Department of Physics, Mathematics and Technologies, Faculty of Humanities and Natural Sciences, University of Prešov, 08001 Prešov, Slovakia)

Abstract

This paper is devoted to some selected topics of the theory of special orthogonal group SO(3). First, we discuss the trace of orthogonal matrices and its relation to the characteristic polynomial; on this basis, the partition of SO(3) formed by conjugation classes is described by trace mapping. Second, we show that every special orthogonal matrix can be expressed as the product of three elementary special orthogonal matrices. Explicit formulas for the decomposition as needed for applications in differential geometry and physics as symmetry transformations are given.

Suggested Citation

  • Demeter Krupka & Ján Brajerčík, 2024. "On the Structure of SO(3): Trace and Canonical Decompositions," Mathematics, MDPI, vol. 12(10), pages 1-28, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1490-:d:1392127
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