Linear Algebra and its Applications最新文献_第10页

P-polynomial and bipartite coherent configurations

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-29 DOI: 10.1016/j.laa.2024.11.027

Sabrina Lato

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Tridiagonal M-matrices whose group inverses are tridiagonal

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-29 DOI: 10.1016/j.laa.2024.11.026

A.M. Encinas , K. Kranthi Priya , K.C. Sivakumar

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Dominant subspace and low-rank approximations from block Krylov subspaces without a prescribed gap

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-28 DOI: 10.1016/j.laa.2024.11.021

Pedro Massey

{"title":"Dominant subspace and low-rank approximations from block Krylov subspaces without a prescribed gap","authors":"Pedro Massey","doi":"10.1016/j.laa.2024.11.021","DOIUrl":"10.1016/j.laa.2024.11.021","url":null,"abstract":"<div><div>We develop a novel convergence analysis of the classical deterministic block Krylov methods for the approximation of <em>h</em>-dimensional dominant subspaces and low-rank approximations of matrices <span><math><mi>A</mi><mo>∈</mo><msup><mrow><mi>K</mi></mrow><mrow><mi>m</mi><mo>×</mo><mi>n</mi></mrow></msup></math></span> (where <span><math><mi>K</mi><mo>=</mo><mi>R</mi></math></span> or <span><math><mi>C</mi><mo>)</mo></math></span> in the case that there is no singular gap at the index <em>h</em> i.e., if <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>h</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> (where <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mo>…</mo><mo>≥</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>≥</mo><mn>0</mn></math></span> denote the singular values of <em>A</em>, and <span><math><mi>p</mi><mo>=</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></span>). Indeed, starting with a (deterministic) matrix <span><math><mi>X</mi><mo>∈</mo><msup><mrow><mi>K</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>r</mi></mrow></msup></math></span> with <span><math><mi>r</mi><mo>≥</mo><mi>h</mi></math></span> satisfying a compatibility assumption with some <em>h</em>-dimensional right dominant subspace of <em>A</em>, we show that block Krylov methods produce arbitrarily good approximations for both problems mentioned above. Our approach is based on recent work by Drineas, Ipsen, Kontopoulou and Magdon-Ismail on the approximation of structural left dominant subspaces. The main difference between our work and previous work on this topic is that instead of exploiting a singular gap at the prescribed index <em>h</em> (which is zero in this case) we exploit the nearest existing singular gaps. We include a section with numerical examples that test the performance of our main results.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"708 ","pages":"Pages 112-149"},"PeriodicalIF":1.0,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164619","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

New existence results for conjoined bases of singular linear Hamiltonian systems with given Sturmian properties 给定Sturmian性质的奇异线性哈密顿系统的连基存在性的新结果

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-26 DOI: 10.1016/j.laa.2024.11.017

Peter Šepitka, Roman Šimon Hilscher

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Graded polynomial identities for the Jordan algebra of 2 × 2 upper triangular matrices

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-26 DOI: 10.1016/j.laa.2024.11.022

Dimas José Gonçalves , Mateus Eduardo Salomão

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The category of quasi-Whittaker modules over the Schrödinger algebra

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-26 DOI: 10.1016/j.laa.2024.11.023

Zhongping Ji , Genqiang Liu , Yueqiang Zhao

引用次数: 0

Stabilization of associated prime ideals of monomial ideals – Bounding the copersistence index 单项式理想的关联素理想的稳定 - 限定共存指数

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-22 DOI: 10.1016/j.laa.2024.11.020

Clemens Heuberger, Jutta Rath, Roswitha Rissner

{"title":"Stabilization of associated prime ideals of monomial ideals – Bounding the copersistence index","authors":"Clemens Heuberger, Jutta Rath, Roswitha Rissner","doi":"10.1016/j.laa.2024.11.020","DOIUrl":"10.1016/j.laa.2024.11.020","url":null,"abstract":"<div><div>The sequence <span><math><msub><mrow><mo>(</mo><mi>Ass</mi><mo>(</mo><mi>R</mi><mo>/</mo><msup><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>)</mo></mrow><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></msub></math></span> of associated primes of powers of a monomial ideal <em>I</em> in a polynomial ring <em>R</em> eventually stabilizes by a known result by Markus Brodmann. Lê Tuân Hoa gives an upper bound for the index where the stabilization occurs. This bound depends on the generators of the ideal and is obtained by separately bounding the powers of <em>I</em> after which said sequence is non-decreasing and non-increasing, respectively. In this paper, we focus on the latter and call the smallest such number the copersistence index. We take up the proof idea of Lê Tuân Hoa, who exploits a certain system of inequalities whose solution sets store information about the associated primes of powers of <em>I</em>. However, these proofs are entangled with a specific choice for the system of inequalities. In contrast to that, we present a generic ansatz to obtain an upper bound for the copersistence index that is uncoupled from this choice of the system. We establish properties for a system of inequalities to be eligible for this approach to work. We construct two suitable inequality systems to demonstrate how this ansatz yields upper bounds for the copersistence index and compare them with Hoa's. One of the two systems leads to an improvement of the bound by an exponential factor.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"707 ","pages":"Pages 162-186"},"PeriodicalIF":1.0,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Characterization of almost-Riordan arrays with row sums 具有行总和的近似瑞尔丹数组的特征

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-22 DOI: 10.1016/j.laa.2024.11.019

Yasemin Alp , E. Gokcen Kocer

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Construction of symplectic solvmanifolds satisfying the hard-Lefschetz condition 构建满足硬-勒夫谢茨条件的交映求解漫域

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-22 DOI: 10.1016/j.laa.2024.11.018

Adrián Andrada, Agustín Garrone

{"title":"Construction of symplectic solvmanifolds satisfying the hard-Lefschetz condition","authors":"Adrián Andrada, Agustín Garrone","doi":"10.1016/j.laa.2024.11.018","DOIUrl":"10.1016/j.laa.2024.11.018","url":null,"abstract":"<div><div>A compact symplectic manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span>. This loosely means that there is a notion of harmonicity of differential forms in <em>M</em>, depending on <em>ω</em> alone, such that every de Rham cohomology class in has a <em>ω</em>-harmonic representative. In this article, we study two non-equivalent families of diagonal almost-abelian Lie algebras that admit a distinguished almost-Kähler structure and compute their cohomology explicitly. We show that they satisfy the hard-Lefschetz condition with respect to any left-invariant symplectic structure by exploiting an unforeseen connection with Kneser graphs. We also show that for some choice of parameters their associated simply connected, completely solvable Lie groups admit lattices, thereby constructing examples of almost-Kähler solvmanifolds satisfying the hard-Lefschetz condition, in such a way that their de Rham cohomology is fully known.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"706 ","pages":"Pages 70-100"},"PeriodicalIF":1.0,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722517","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

Laplacian energies of vertices 顶点的拉普拉卡能量

IF 1 3区数学

Linear Algebra and its Applications Pub Date : 2024-11-19 DOI: 10.1016/j.laa.2024.11.016

J. Guerrero

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