Ranks derived from multilinear maps

DOI10.1016/j.jpaa.2010.11.010zbMath1215.15029OpenAlexW2003779161WikidataQ60547192 ScholiaQ60547192MaRDI QIDQ534026

Enrico Carlini, Johannes Kleppe

Publication date: 10 May 2011

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2010.11.010

zbMATH Keywords

tensorranksvector spacesSegre varietiessecant varietiesmultilinear maps

Mathematics Subject Classification ID

Special varieties (14M99) Multilinear algebra, tensor calculus (15A69)

Related Items (8)

Polynomial foldings and rank of tensors ⋮ Tensor Completion in Hierarchical Tensor Representations ⋮ Rank-1 Tensor Properties with Applications to a Class of Tensor Optimization Problems ⋮ Discrete Fourier Transform Tensors and Their Ranks ⋮ An algorithm for the non-identifiability of rank-3 tensors ⋮ The number of singular vector tuples and uniqueness of best rank-one approximation of tensors ⋮ On partial and generic uniqueness of block term tensor decompositions ⋮ The Hackbusch conjecture on tensor formats. II.

Cites Work

• Unnamed Item
• On the ranks and border ranks of symmetric tensors
• Rank and optimal computation of generic tensors
• Ranks of tensors, secant varieties of Segre varieties and fat points
• Erratum to: ``Ranks of tensors, secant varieties of Segre varieties and fat points
• Ranks of tensors and a generalization of secant varieties
• Secant varieties of ℙ¹×⋯×ℙ¹ (𝕟-times) are NOT defective for 𝕟≥5
• The border rank of the multiplication of $2\times 2$ matrices is seven
• Induction for secant varieties of Segre varieties
• A Multilinear Singular Value Decomposition

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