Typical ranks ofm×n× (m− 1)ntensors with 3 ≤m≤nover the real number field

DOI10.1080/03081087.2014.910206zbMath1310.15043arXiv1210.6713OpenAlexW2138887611MaRDI QIDQ5175371

Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki

Publication date: 20 February 2015

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6713

zbMATH Keywords

tensortypical rankperfectthree-way arrayHurwitz-Radon number

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (3)

Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals ⋮ Unnamed Item ⋮ Typical ranks of semi-tall real 3-tensors

Cites Work

• On the generic and typical ranks of 3-tensors
• Rank of 3-tensors with 2 slices and Kronecker canonical forms
• Generic and typical ranks of multi-way arrays
• Rank and optimal computation of generic tensors
• Simplicity of core arrays in three-way principal component analysis and the typical rank of \(p\times q\times 2\) arrays
• Effective Noether irreducibility forms and applications
• Typical ranks for \(m\times n\times (m-1)n\) tensors with \(m \leq n\)
• The typical rank of tall three-way arrays
• The Lax conjecture is true
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• A Note on Hyperbolic Polynomials.

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