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Mathematics
Special Issues
Spectral Theory of Tensors, Tensor (Rank) Decompositions, and Their Applications
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Spectral Theory of Tensors, Tensor (Rank) Decompositions, and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 1209

Special Issue Editors

Prof. Dr. Tan Zhang

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Guest Editor
Department of Mathematics & Statistics, Murray State University, Murray, KY 42071-0009, USA
Interests: linear and multilinear algebra; differential geometry; algebraic topology
Prof. Dr. Shenglong Hu

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Guest Editor
Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
Interests: tensor eigenvalue problems; hypergraph theory; numerical linear algebra

Special Issue Information

Dear Colleagues,

The study of higher-order tensors (multi-dimensional arrays) has been an active research area for over a decade. Numerous significant progresses have been made in the front on eigenvalue problems for tensors, tensor rank problems, tensor decompositions problems, and spectral hypergraph theory,  just to name a few, while new discoveries are being made as we speak. Alongside theoretical development, a wide range of applications found their way in Numerical Multilinear Algebra, Image Processing, Statistical Data Analysis, Multi-relational data mining, best rank-one approximation, Convex Optimizations, Higher-order Markov chains, and Quantum entanglement problems, etc.

Prof. Dr. Tan Zhang
Prof. Dr. Shenglong Hu
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • tensor eigenvalues
  • tensor ranks
  • tensor decompositions
  • spectral hypergraph theory
  • positive semi-definite programming
  • higher-order Markov chains

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Published Papers (2 papers)

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Research

9 pages, 230 KiB  
Article
The ασ-Approximation Property and Its Related Operator Ideals
by Ju Myung Kim
Mathematics 2024, 12(13), 2006; https://doi.org/10.3390/math12132006 - 28 Jun 2024
Viewed by 272
Abstract
In this paper, we study the σ-tensor norm (ασ), the absolutely τ-summing operator and the σ-nuclear operator. We characterize the ασ-approximation property in terms of some density of the space of absolutely τ-summing operators. [...] Read more.
In this paper, we study the σ-tensor norm (ασ), the absolutely τ-summing operator and the σ-nuclear operator. We characterize the ασ-approximation property in terms of some density of the space of absolutely τ-summing operators. When X* or Y*** has the approximation property, we prove that an operator T from X to Y is σ-nuclear if the adjoint of T is σ-nuclear. Full article
(This article belongs to the Special Issue Spectral Theory of Tensors, Tensor (Rank) Decompositions, and Their Applications)
18 pages, 287 KiB  
Article
The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point
by Kelly Pearson and Tan Zhang
Mathematics 2024, 12(5), 705; https://doi.org/10.3390/math12050705 - 28 Feb 2024
Viewed by 528
Abstract
We begin with a degree m real homogeneous polynomial in n indeterminants and bound the distance from a given n-dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous polynomial associated with [...] Read more.
We begin with a degree m real homogeneous polynomial in n indeterminants and bound the distance from a given n-dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous polynomial associated with a nonzero m-order n-dimensional weakly symmetric tensor which has zero as an eigenvalue. We provide “nested spheres” conditions to bound the distance from a given n-dimensional real vector to the nearest zero eigenvector. Full article
(This article belongs to the Special Issue Spectral Theory of Tensors, Tensor (Rank) Decompositions, and Their Applications)
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