Linear Algebra and its Applications最新文献_第9页

A generalization of Fiedler's lemma and its applications 费德勒定理的推广及其应用

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-14 DOI: 10.1016/j.laa.2024.07.008

Yangyang Wu, Xiaoling Ma

引用次数: 0

On the invertibility of matrices with a double saddle-point structure 论具有双鞍点结构的矩阵的可逆性

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-11 DOI: 10.1016/j.laa.2024.07.005

Fatemeh P.A. Beik , Chen Greif , Manfred Trummer

引用次数: 0

Anzahl theorems for trivially intersecting subspaces generating a non-singular subspace I: Symplectic and hermitian forms 生成非星形子空间的微相交子空间的安扎尔定理 I：交映和赫米提形式

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-09 DOI: 10.1016/j.laa.2024.07.004

Maarten De Boeck , Geertrui Van de Voorde

引用次数: 0

Representations of the C-series related to the q-analog Virasoro-like Lie algebra 与 q-analog Virasoro-like Lie algebra 有关的 [公式省略] 系列的表示

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-06 DOI: 10.1016/j.laa.2024.06.028

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引用次数: 0

A low-rank ODE for spectral clustering stability 光谱聚类稳定性的低阶 ODE

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-06 DOI: 10.1016/j.laa.2024.07.001

Nicola Guglielmi, Stefano Sicilia

{"title":"A low-rank ODE for spectral clustering stability","authors":"Nicola Guglielmi, Stefano Sicilia","doi":"10.1016/j.laa.2024.07.001","DOIUrl":"https://doi.org/10.1016/j.laa.2024.07.001","url":null,"abstract":"Spectral clustering is a well-known technique which identifies clusters in an undirected graph, with vertices and weight matrix , by exploiting its graph Laplacian . In particular, the clusters can be identified by the knowledge of the eigenvectors associated with the smallest non zero eigenvalues of , say (recall that ). Identifying is an essential task of a clustering algorithm, since if is close to the reliability of the method is reduced. The -th spectral gap is often considered as a stability indicator. This difference can be seen as an unstructured distance between and an arbitrary symmetric matrix with vanishing -th spectral gap. A more appropriate structured distance to ambiguity such that represents the Laplacian of a graph has been proposed in Andreotti et al. (2021) . This is defined as the minimal distance between and Laplacians of graphs with the same vertices and edges, but with weights that are perturbed such that the -th spectral gap vanishes. In this article we consider a slightly different approach, still based on the reformulation of the problem into the minimization of a suitable functional in the eigenvalues. After determining the gradient system associated with this functional, we introduce a low-rank projected system, suggested by the underlying low-rank structure of the extremizers of the problem. The integration of this low-rank system, requires both a moderate computational effort and a memory requirement, as it is shown in some illustrative numerical examples.","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587729","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

Positive vectors, pairwise comparison matrices and directed Hamiltonian cycles 正向量、成对比较矩阵和有向哈密顿循环

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-06 DOI: 10.1016/j.laa.2024.07.003

引用次数: 0

P-matrix powers P 矩阵幂

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-06 DOI: 10.1016/j.laa.2024.07.002

引用次数: 0

On the cohomology of restricted Heisenberg Lie algebras 论受限海森堡李代数的同调性

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-03 DOI: 10.1016/j.laa.2024.06.027

引用次数: 0

Excessive symmetry can preclude cutoff 对称性过强可能导致无法截断

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-01 DOI: 10.1016/j.laa.2024.06.025

Eric Ramos , Graham White

引用次数: 0

Strong consistency of an estimator by the truncated singular value decomposition for an errors-in-variables regression model with collinearity 具有共线性的变量误差回归模型的截断奇异值分解估计器的强一致性

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2024-07-01 DOI: 10.1016/j.laa.2024.06.024

Kensuke Aishima

引用次数: 0