Schur complements for tensors and multilinear commutative rank
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915854625538048 |
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| author | Moshkovitz, Guy Zhu, Daniel G. |
| author_facet | Moshkovitz, Guy Zhu, Daniel G. |
| contents | We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin and Reutenauer, answers a question of Lampert on the relation between the analytic and slice ranks of trilinear forms, and establishes a special case of the conjecture that the analytic and partition ranks of a tensor are equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11038 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schur complements for tensors and multilinear commutative rank Moshkovitz, Guy Zhu, Daniel G. Combinatorics Commutative Algebra 15A69 (Primary) 11B30, 68R05 (Secondary) We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin and Reutenauer, answers a question of Lampert on the relation between the analytic and slice ranks of trilinear forms, and establishes a special case of the conjecture that the analytic and partition ranks of a tensor are equivalent. |
| title | Schur complements for tensors and multilinear commutative rank |
| topic | Combinatorics Commutative Algebra 15A69 (Primary) 11B30, 68R05 (Secondary) |
| url | https://arxiv.org/abs/2603.11038 |