Computing Left Eigenvalues of Quaternion Matrices
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912931442065408 |
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| author | Sebek, Michael |
| author_facet | Sebek, Michael |
| contents | We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature examples and benchmark ensembles, together with a compact MATLAB reference implementation, demonstrate reproducible, certificate-based computations up to size 64x64, including the detection of multiple spherical components and non-generic phenomena such as more than n isolated left eigenvalues and left-spectrum deficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing Left Eigenvalues of Quaternion Matrices Sebek, Michael Rings and Algebras 15A33, 15A18, 65F15, 65H10 We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature examples and benchmark ensembles, together with a compact MATLAB reference implementation, demonstrate reproducible, certificate-based computations up to size 64x64, including the detection of multiple spherical components and non-generic phenomena such as more than n isolated left eigenvalues and left-spectrum deficiency. |
| title | Computing Left Eigenvalues of Quaternion Matrices |
| topic | Rings and Algebras 15A33, 15A18, 65F15, 65H10 |
| url | https://arxiv.org/abs/2603.00018 |