On the Structure of SO(3): Trace and Canonical Decompositions-Reference-Cited by-同舟云学术

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

Published:2024-05-10 Issue:10 Volume:12 Page:1490
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Krupka Demeter¹,Brajerčík Ján¹²^ORCID

Affiliation:

1. Lepage Research Institute, 08001 Prešov, Slovakia

2. 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.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/10/1490/pdf

Reference4 articles.

1. Krupka, D., and Brajerčík, J. (2022). Schwarzschild spacetimes: Topology. Axioms, 11.

2. Alperin, J.L., and Bell, R.B. (1995). Groups and Representations, Springer. Graduate Texts in Mathematics 162.

3. Kurosh, A. (1980). Higher Algebra, Mir Publishers.

4. Bui, H.T.A. (2020). Classifying the Finite Subgroups of SO(3), The University of Chicago, Department of Mathematics. Unpublished work.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Explicit Parameterizations of Ortho-Symplectic Matrices in R4;Mathematics;2024-08-06