On solutions of singular Sylvester equations in quaternions
Rings and Algebras
2026-05-08 v6
Abstract
The quaternionic equations ax-xb=0 and ax-xb=c are investigated, which are called homogeneous and inhomogeneous Sylvester equations, respectively. Conditions for the existence of solutions are provided. In addition, the general and nonzero solutions to these equations are derived applying quaternion square roots.
Keywords
Cite
@article{arxiv.2510.04629,
title = {On solutions of singular Sylvester equations in quaternions},
author = {Hristina Radak and Christian Scheunert and Frank H. P. Fitzek},
journal= {arXiv preprint arXiv:2510.04629},
year = {2026}
}