Algebraic Methods for Tensor Data

DOI10.1137/19M1272494zbMath1457.15026arXiv2005.12988OpenAlexW3120455526MaRDI QIDQ5148409

Neriman Tokcan, Kayvan Najarian, Jonathan Gryak, H. G. J. Derksen

Publication date: 4 February 2021

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.12988

zbMATH Keywords

spectral normtensorsBrauer diagrams

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Vector and tensor algebra, theory of invariants (15A72) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Multilinear algebra, tensor calculus (15A69)

Uses Software

• TensorToolbox
• OEIS

Cites Work

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• On tensor completion via nuclear norm minimization
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• On algebras which are connected with the semisimple continuous groups
• Exact matrix completion via convex optimization
• Rank-One Approximation to High Order Tensors
• Bounds on the Spectral Norm and the Nuclear Norm of a Tensor Based on Tensor Partitions
• Tensor rank is NP-complete
• A Multilinear Singular Value Decomposition
• Nuclear norm of higher-order tensors
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• On Orthogonal Tensors and Best Rank-One Approximation Ratio
• Most Tensor Problems Are NP-Hard
• A Theory of Cross-Spaces. (AM-26)
• Produits tensoriels topologiques et espaces nucléaires