On solutions of singular Sylvester equations in quaternions

Q: What type of study is this?

This is a Quantitative Study study.

Hristina Radak; Christian Scheunert; Frank H. P. Fitzek

doi:10.48550/arxiv.2510.04629

October 6, 2025Open Access

On solutions of singular Sylvester equations in quaternions

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Key Points

The study identifies conditions necessary for the existence of solutions to Sylvester equations.
It provides derivations for both general and nonzero solutions using quaternion square roots.
Homogeneous equations take the form ax-xb=0, while inhomogeneous ones are ax-xb=c.
Understanding these solutions is crucial for advancing quaternion mathematics and its applications.

Implication

Analysis reveals conditions for solutions of homogeneous and inhomogeneous Sylvester equations.

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.

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Cite This Study

Radak et al. (2025) studied this question.

synapsesocial.com/papers/68e861857ef2f04ca37e39b4 https://doi.org/10.48550/arxiv.2510.04629

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On solutions of singular Sylvester equations in quaternions

Key Points

Implication

Abstract

Discussion

Cite This Study

On solutions of singular Sylvester equations in quaternions

Key Points

Implication

Abstract

Discussion

Cite This Study

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