About the maximal rank of 3-tensors over the real and the complex number field

DOI10.1007/s10463-010-0294-5zbMath1440.15020arXiv0806.4048OpenAlexW2142934180MaRDI QIDQ2634810

Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki

Publication date: 19 February 2016

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4048

zbMATH Keywords

tensormaximal rank

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Multilinear algebra, tensor calculus (15A69)

Related Items (8)

Approximation by matrices with simple spectra ⋮ A note on the maximal rank ⋮ Maximal Rank of ${m}\times{n}\times 2$ Tensors over Arbitrary Fields ⋮ Typical ranks for \(m\times n\times (m-1)n\) tensors with \(m \leq n\) ⋮ Bad and good news for Strassen's laser method: border rank of \(\mathrm{Perm}_3\) and strict submultiplicativity ⋮ Unnamed Item ⋮ On maximum, typical and generic ranks ⋮ On Strassen's Rank Additivity for Small Three-way Tensors

Cites Work

• Unnamed Item
• Tensor Decompositions and Applications
• Rank of 3-tensors with 2 slices and Kronecker canonical forms
• On the maximal multiplicative complexity of a family of bilinear forms
• Survey on tensor signal algebraic filtering
• Bounds on the ranks of some 3-tensors
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

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