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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/2508.19902 |
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| _version_ | 1866915797524283392 |
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| author | Kulkarni, Ayush Colley, Charles Gleich, David F. |
| author_facet | Kulkarni, Ayush Colley, Charles Gleich, David F. |
| contents | We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant eigenvector of a Kronecker product decouples into a product of eigenvectors of the tensors underlying the Kronecker product. This does not occur for H-eigenvectors and indeed, the largest H-eigenvalue can exceed the product of the H-eigenvalues of the component tensors. Beyond this general counterexample, we show this decoupling does hold in the case of diagonal tensors as well as nonnegative tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple Kulkarni, Ayush Colley, Charles Gleich, David F. Numerical Analysis We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant eigenvector of a Kronecker product decouples into a product of eigenvectors of the tensors underlying the Kronecker product. This does not occur for H-eigenvectors and indeed, the largest H-eigenvalue can exceed the product of the H-eigenvalues of the component tensors. Beyond this general counterexample, we show this decoupling does hold in the case of diagonal tensors as well as nonnegative tensors. |
| title | Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.19902 |