A new \(Z\)-eigenvalue localization set for tensors

DOI10.1186/s13660-017-1363-6zbMath1366.15009OpenAlexW2605627654WikidataQ33592116 ScholiaQ33592116MaRDI QIDQ523903

Jianxing Zhao

Publication date: 24 April 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-017-1363-6

zbMATH Keywords

spectral radiusweakly symmetricnonnegative tensors\(Z\)-eigenvaluelocalization set

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69)

Related Items (20)

Two \(S\)-type \( Z\)-eigenvalue inclusion sets for tensors ⋮ Further results for \(Z\)-eigenvalue localization theorem for higher-order tensors and their applications ⋮ Pareto \(Z\)-eigenvalue inclusion theorems for tensor eigenvalue complementarity problems ⋮ New \(Z\)-eigenvalue localization sets for tensors with applications ⋮ \(Z\)-eigenvalue exclusion theorems for tensors ⋮ \(E\)-eigenvalue localization sets for tensors ⋮ A new Brauer-type \(Z\)-eigenvalue inclusion set for even-order tensors ⋮ Z-eigenvalue localization sets for tensors and the applications in rank-one approximation and quantum entanglement ⋮ New \(S\)-type localization sets for \(C\)-eigenvalues of a piezoelectric-type tensor ⋮ New \(Z\)-eigenvalue inclusion theorem of tensors with application to the geometric measure of entanglement ⋮ Optimal \(Z\)-eigenvalue inclusion intervals for even order tensors and their applications ⋮ A new Brauer-type \(Z\)-eigenvalue inclusion set for tensors ⋮ An \(S\)-type inclusion set for \(C\)-eigenvalues of a piezoelectric-type tensor ⋮ \(Z\)-eigenvalue localization sets for even order tensors and their applications ⋮ \(M\)-eigenvalues-based sufficient conditions for the positive definiteness of fourth-order partially symmetric tensors ⋮ Z-eigenvalues-based sufficient conditions for the positive definiteness of fourth-order tensors ⋮ \(E\)-eigenvalue localization sets for fourth-order tensors ⋮ Optimal \(Z\)-eigenvalue inclusion intervals of tensors and their applications ⋮ New sufficient condition for the positive definiteness of fourth order tensors ⋮ E-eigenvalue inclusion theorems for tensors

Cites Work

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• Bounds for the Z-eigenpair of general nonnegative tensors
• Some variational principles for \(Z\)-eigenvalues of nonnegative tensors
• \(Z\)-eigenpair bounds for an irreducible nonnegative tensor
• \(Z\)-eigenvalue inclusion theorems for tensors
• Upper bound for the largest \(Z\)-eigenvalue of positive tensors
• A new eigenvalue inclusion set for tensors and its applications
• Eigenvalues of a real supersymmetric tensor
• An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors
• A new Brauer-type eigenvalue localization set for tensors
• New eigenvalue inclusion sets for tensors
• Upper Bounds for the Z-spectral Radius of Nonnegative Tensors
• Spectral Properties of Positively Homogeneous Operators Induced by Higher Order Tensors

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