Linear Algebra and its Applications最新文献_第5页

On the regularity of the language of some T-ideals 论某些t理想的语言的规律性

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-08-06 DOI: 10.1016/j.laa.2025.08.002

Lucio Centrone , Alexei Kanel-Belov , Roberto La Scala

引用次数: 0

A hidden variable resultant method for the polynomial multiparameter eigenvalue problem 多项式多参数特征值问题的隐变量合成法

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-08-05 DOI: 10.1016/j.laa.2025.07.031

Emil Graf, Alex Townsend

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Extremal properties and bounds for the generalized algebraic connectivity of graphs in Euclidean spaces 欧几里德空间中图的广义代数连通性的极值性质和界

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-08-05 DOI: 10.1016/j.laa.2025.07.028

J. Ignacio Alvarez-Hamelin , Juan I. Giribet , Ignacio Mas , J. Francisco Presenza

{"title":"Extremal properties and bounds for the generalized algebraic connectivity of graphs in Euclidean spaces","authors":"J. Ignacio Alvarez-Hamelin , Juan I. Giribet , Ignacio Mas , J. Francisco Presenza","doi":"10.1016/j.laa.2025.07.028","DOIUrl":"10.1016/j.laa.2025.07.028","url":null,"abstract":"<div><div>This article contributes to the study of graph rigidity and its interplay with fundamental graph invariants. Recently, a quantitative measure of graph rigidity in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, termed the generalized algebraic connectivity, was introduced. This development extends the notion of algebraic connectivity—the second-smallest eigenvalue of the Laplacian matrix. In this work, we show that the generalized algebraic connectivity is bounded above by the algebraic connectivity. To capture this relationship, we introduce the <em>d</em>-rigidity ratio, a normalized metric of a graph's rigidity relative to its connectivity. We also investigate the relationship between rigidity and the diameter. In this context, we provide the maximal diameter achievable by rigid graphs and show that generalized path graphs serve as extremal examples. Moreover, we establish a new upper bound for the algebraic connectivity that depends inversely on the diameter and the vertex connectivity. Finally, we derive an upper bound for the algebraic connectivity of generalized path graphs that asymptotically improves existing ones by a factor of four.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"727 ","pages":"Pages 24-36"},"PeriodicalIF":1.1,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Symmetries of hypergraphs and some invariant subspaces of matrices associated with hypergraphs 超图的对称性及与超图相关的矩阵的不变子空间

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-08-05 DOI: 10.1016/j.laa.2025.07.030

Anirban Banerjee , Samiron Parui

引用次数: 0

Unique continuation principles for finite-element discretizations of the Laplacian 拉普拉斯有限元离散化的独特延拓原理

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-08-05 DOI: 10.1016/j.laa.2025.07.029

Graham Cox, Scott MacLachlan, Luke Steeves

{"title":"Unique continuation principles for finite-element discretizations of the Laplacian","authors":"Graham Cox, Scott MacLachlan, Luke Steeves","doi":"10.1016/j.laa.2025.07.029","DOIUrl":"10.1016/j.laa.2025.07.029","url":null,"abstract":"<div><div>Unique continuation principles are fundamental properties of elliptic partial differential equations, giving conditions that guarantee that the solution to an elliptic equation must be uniformly zero. Since finite-element discretizations are a natural tool to help gain understanding into elliptic equations, it is natural to ask if such principles also hold at the discrete level. In this work, we prove a version of the unique continuation principle for piecewise-linear and -bilinear finite-element discretizations of the Laplacian eigenvalue problem on polygonal domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Namely, we show that any solution to the discretized equation <span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>λ</mi><mi>u</mi></math></span> with vanishing Dirichlet and Neumann traces must be identically zero under certain geometric and topological assumptions on the resulting triangulation. We also provide a counterexample, showing that a nonzero <em>inner solution</em> exists when the topological assumptions are not satisfied. Finally, we give an application to an eigenvalue interlacing problem, where the space of inner solutions makes an explicit appearance.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"727 ","pages":"Pages 84-111"},"PeriodicalIF":1.1,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Maximizing the spectral radius of graphs of given size with a forbidden subgraph 用禁止子图最大化给定大小的图的谱半径

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-08-05 DOI: 10.1016/j.laa.2025.07.032

Yanting Zhang , Ligong Wang

引用次数: 0

Group gradings on finite-dimensional incidence algebras. II 有限维关联代数上的群分级。2

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-07-31 DOI: 10.1016/j.laa.2025.07.027

Helen Samara Dos Santos , Felipe Yukihide Yasumura

引用次数: 0

Majorizations for probability distributions, column stochastic matrices and their linear preservers 概率分布的多数化，列随机矩阵及其线性保持器

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-07-28 DOI: 10.1016/j.laa.2025.07.024

Pavel Shteyner

引用次数: 0

New weighted spectral geometric mean and quantum divergence 新的加权谱几何平均和量子散度

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-07-28 DOI: 10.1016/j.laa.2025.07.025

Miran Jeong , Sejong Kim , Tin-Yau Tam

引用次数: 0

Doubly transitive equiangular tight frames that contain regular simplices 包含正则单形的双传递等角紧框架

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2025-07-28 DOI: 10.1016/j.laa.2025.07.023

Matthew Fickus, Evan C. Lake

{"title":"Doubly transitive equiangular tight frames that contain regular simplices","authors":"Matthew Fickus, Evan C. Lake","doi":"10.1016/j.laa.2025.07.023","DOIUrl":"10.1016/j.laa.2025.07.023","url":null,"abstract":"<div><div>An equiangular tight frame (ETF) is a finite sequence of equal norm vectors in a Hilbert space that achieves equality in the Welch bound, and so has minimal coherence. The binder of an ETF is the set of all subsets of its indices whose corresponding vectors form a regular simplex. An ETF achieves equality in Donoho and Elad's spark bound if and only if its binder is nonempty. When this occurs, its binder is the set of all linearly dependent subsets of it of minimal size. Moreover, if members of the binder form a balanced incomplete block design (BIBD) then its incidence matrix can be phased to produce a sparse representation of its dual (Naimark complement). A few infinite families of ETFs are known to have this remarkable property. In this paper, we relate this property to the recently introduced concept of a doubly transitive equiangular tight frame (DTETF), namely an ETF for which the natural action of its symmetry group is doubly transitive. In particular, we show that the binder of any DTETF is either empty or forms a BIBD, and moreover that when the latter occurs, any member of the binder of its dual is an oval of this BIBD. We then apply this general theory to certain known infinite families of DTETFs. Specifically, any symplectic form on a finite vector space yields a DTETF, and we compute the binder of it and its dual, showing that the former is empty except in a single notable case, and that the latter consists of affine Lagrangian subspaces. This unifies and generalizes several results from the existing literature. We then consider the binders of four infinite families of DTETFs that arise from quadratic forms over the field of two elements, showing that two of these are empty except in a finite number of cases, whereas the other two form BIBDs that relate to each other, and to Lagrangian subspaces, in nonobvious ways.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 113-163"},"PeriodicalIF":1.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0