Typical ranks of semi-tall real 3-tensors

DOI10.1080/03081087.2019.1637811zbMath1470.15020arXiv1705.02768OpenAlexW2963831289WikidataQ114100595 ScholiaQ114100595MaRDI QIDQ5005286

Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki

Publication date: 9 August 2021

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

Full work available at URL: https://arxiv.org/abs/1705.02768

zbMATH Keywords

tensor rankdeterminantal varietytypical rankBezout's theoremsemi-tall tensortall tensor

Mathematics Subject Classification ID

Linkage, complete intersections and determinantal ideals (13C40) Determinantal varieties (14M12) Semialgebraic sets and related spaces (14P10) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03)

Cites Work

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• Algebraic and computational aspects of real tensor ranks
• Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals
• Ranks of tensors, secant varieties of Segre varieties and fat points
• Typical ranks for \(m\times n\times (m-1)n\) tensors with \(m \leq n\)
• The typical rank of tall three-way arrays
• On the ideals of secant varieties to certain rational varieties
• Typical ranks of certain 3-tensors and absolutely full column rank tensors
• Typical ranks ofm×n× (m− 1)ntensors with 3 ≤m≤nover the real number field

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