On solutions of singular Sylvester equations in quaternions

2025/10/06 by Radak, Hristina, Scheunert, Christian, Fitzek, Frank H. P. · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.04629

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.

Citations

• Basis-free Solution to General Linear Quaternionic Equation

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• A Closed-form Solution to the Wahba Problem for Pairwise Similar Quaternions

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