On solutions of singular Sylvester equations in quaternions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866911656070610944 |
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| author | Radak, Hristina Scheunert, Christian Fitzek, Frank H. P. |
| author_facet | Radak, Hristina Scheunert, Christian Fitzek, Frank H. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On solutions of singular Sylvester equations in quaternions Radak, Hristina Scheunert, Christian Fitzek, Frank H. P. Rings and Algebras 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. |
| title | On solutions of singular Sylvester equations in quaternions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2510.04629 |