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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05836 |
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| _version_ | 1866915483154907136 |
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| author | Stessin, Michael Yang, Rongwei |
| author_facet | Stessin, Michael Yang, Rongwei |
| contents | If a tuple of matrices has a common invariant subspace, its projective joint spectrum has an algebraic component. In general, the converse is not true, and there might be algebraic components in the projective joint spectrum without corresponding common invariant subspaces. In this paper we give necessary and sufficient conditions for the occurrence of such correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral test of reducibility for Matrix tuples Stessin, Michael Yang, Rongwei Functional Analysis If a tuple of matrices has a common invariant subspace, its projective joint spectrum has an algebraic component. In general, the converse is not true, and there might be algebraic components in the projective joint spectrum without corresponding common invariant subspaces. In this paper we give necessary and sufficient conditions for the occurrence of such correspondence. |
| title | Spectral test of reducibility for Matrix tuples |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.05836 |