A concise proof to the spectral and nuclear norm bounds through tensor partitions

DOI10.1515/math-2019-0028zbMath1430.15017OpenAlexW2944972425WikidataQ127829069 ScholiaQ127829069MaRDI QIDQ2278368

Xu Kong

Publication date: 5 December 2019

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/math-2019-0028

zbMATH Keywords

spectral normnuclear normtensor normtensor partition

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Multilinear algebra, tensor calculus (15A69)

Related Items (1)

Algebraic Methods for Tensor Data

Cites Work

• Tensor Decompositions and Applications
• On tensor completion via nuclear norm minimization
• Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
• Some bounds for the spectral radius of nonnegative tensors
• Perron-Frobenius theorem for nonnegative tensors
• Combinatorial methods for the spectral \(p\)-norm of hypermatrices
• Bounds on the Spectral Norm and the Nuclear Norm of a Tensor Based on Tensor Partitions
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Nuclear norm of higher-order tensors
• New eigenvalue inclusion sets for tensors
• On the Uniqueness and Perturbation to the Best Rank-One Approximation of a Tensor
• Tensor Analysis

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