Z-eigenvalue localization sets for tensors and the applications in rank-one approximation and quantum entanglement

DOI10.1007/s10440-023-00589-zzbMath1517.15020OpenAlexW4383263389MaRDI QIDQ6171708

No author found.

Publication date: 14 August 2023

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-023-00589-z

zbMATH Keywords

spectral radiusgeometric measuresZ-eigenvaluethe best rank-one approximation

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69) Quantum coherence, entanglement, quantum correlations (81P40)

Cites Work

• Tensor Decompositions and Applications
• On the convergence of a greedy rank-one update algorithm for a class of linear systems
• Some variational principles for \(Z\)-eigenvalues of nonnegative tensors
• \(Z\)-eigenpair bounds for an irreducible nonnegative tensor
• A new \(Z\)-eigenvalue localization set for tensors
• \(Z\)-eigenvalue inclusion theorems for tensors
• Further results for \(Z\)-eigenvalue localization theorem for higher-order tensors and their applications
• \(Z\)-eigenvalue inclusion theorem of tensors and the geometric measure of entanglement of multipartite pure states
• How entangled can a multi-party system possibly be?
• Two \(S\)-type \( Z\)-eigenvalue inclusion sets for tensors
• Eigenvalues of a real supersymmetric tensor
• Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines
• Numerical multilinear algebra and its applications
• An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors
• The Best Rank-One Approximation Ratio of a Tensor Space
• On the successive supersymmetric rank-1 decomposition of higher-order supersymmetric tensors
• Finding the Largest Eigenvalue of a Nonnegative Tensor
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Tensor Decomposition for Signal Processing and Machine Learning
• Most boson quantum states are almost maximally entangled
• The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
• Highly entangled tensors
• Matrix permanent and quantum entanglement of permutation invariant states
• The geometric measure of multipartite entanglement and the singular values of a hypermatrix
• On the Uniqueness and Perturbation to the Best Rank-One Approximation of a Tensor
• On the limiting probability distribution of a transition probability tensor
• Spectral Properties of Positively Homogeneous Operators Induced by Higher Order Tensors

This page was built for publication: Z-eigenvalue localization sets for tensors and the applications in rank-one approximation and quantum entanglement