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- Title
A General Approach to Sylvester-Polynomial-Conjugate Matrix Equations.
- Authors
Mazurek, Ryszard
- Abstract
Sylvester-polynomial-conjugate matrix equations unify many well-known versions and generalizations of the Sylvester matrix equation A X − X B = C which have a wide range of applications. In this paper, we present a general approach to Sylvester-polynomial-conjugate matrix equations via groupoids, vector spaces, and matrices over skew polynomial rings. The obtained results are applied to Sylvester-polynomial-conjugate matrix equations over complex numbers and quaternions. The main role in our approach is played by skew polynomial rings, which are well-known tools in algebra to provide examples of asymmetry between left-sided and right-sided versions of many ring objects.
- Subjects
SYLVESTER matrix equations; POLYNOMIAL rings; VECTOR spaces; COMPLEX numbers; EQUATIONS; GROUPOIDS
- Publication
Symmetry (20738994), 2024, Vol 16, Issue 2, p246
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym16020246