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

Demeter Krupka and Ján Brajerčík ()
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Demeter Krupka: Lepage Research Institute, 08001 Prešov, Slovakia
Ján Brajerčík: Lepage Research Institute, 08001 Prešov, Slovakia

Mathematics, 2024, vol. 12, issue 10, 1-25

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.

Keywords: special orthogonal group; orbit stabilizer; trace; SO(3) matrix decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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