Lower bounds on the rank and symmetric rank of real tensors

DOI10.1016/j.jsc.2023.01.004OpenAlexW4318275258MaRDI QIDQ2701028

Kexin Wang, Anna Leah Seigal

Publication date: 27 April 2023

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.11740

zbMATH Keywords

tensor decompositiontensor rankComon's conjecture

Mathematics Subject Classification ID

Miscellaneous inequalities involving matrices (15A45) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03) Secant varieties, tensor rank, varieties of sums of powers (14N07)

Related Items (1)

More on Tensors with Different Rank and Symmetric Rank

Uses Software

• TensorToolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• CUR matrix decompositions for improved data analysis
• Operator norm inequalities between tensor unfoldings on the partition lattice
• On the ranks and border ranks of symmetric tensors
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• The solution to the Waring problem for monomials and the sum of coprime monomials
• On the rank and the approximation of symmetric tensors
• Counterexamples to Strassen's direct sum conjecture
• On Comon's conjecture over arbitrary fields
• Ranks and symmetric ranks of cubic surfaces
• On the real rank of monomials
• Remarks on the Symmetric Rank of Symmetric Tensors
• Comon's Conjecture, Rank Decomposition, and Symmetric Rank Decomposition of Symmetric Tensors
• Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture
• Tensor decompositions for learning latent variable models
• Tensor Spaces and Numerical Tensor Calculus
• A Counterexample to Comon's Conjecture
• Algebraic Statistics
• Duality of graphical models and tensor networks
• On Uniqueness and Computation of the Decomposition of a Tensor into Multilinear Rank-$(1,L_r,L_r)$ Terms
• Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank
• Polynomials and tensors of bounded strength
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Symmetric Tensors and Symmetric Tensor Rank
• Geometry and Complexity Theory
• Most Tensor Problems Are NP-Hard
• Geometric complexity theory and tensor rank

This page was built for publication: Lower bounds on the rank and symmetric rank of real tensors