{"title":"Spectral radius and fractional [a,b]-factor of graphs","authors":"Yuang Li , Dandan Fan , Yinfen Zhu","doi":"10.1016/j.laa.2025.03.012","DOIUrl":"10.1016/j.laa.2025.03.012","url":null,"abstract":"<div><div>Let <span><math><mi>h</mi><mo>:</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> be a function on <span><math><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and let <span><math><mi>a</mi><mo>,</mo><mi>b</mi></math></span> be two positive integers with <span><math><mi>a</mi><mo>≤</mo><mi>b</mi></math></span>. If <span><math><mi>a</mi><mo>≤</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msub><mi>h</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>≤</mo><mi>b</mi></math></span> for any <span><math><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, then the spanning subgraph with edge set <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>=</mo><mo>{</mo><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mi>h</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>}</mo></math></span>, denoted by <span><math><mi>G</mi><mrow><mo>[</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>]</mo></mrow></math></span>, is called a fractional <span><math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span>-factor of <em>G</em> with indicator function <em>h</em>. In this paper, we provide a spectral condition to guarantee the existence of a fractional <span><math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span>-factor in a graph with minimum degree <span><math><mi>δ</mi><mo>≥</mo><mi>a</mi><mo>≥</mo><mn>1</mn></math></span>, which extends some previous results. Moreover, we also provide a lower bound on the size of a graph to guarantee the existence of a fractional <span><math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span>-factor for <span><math><mi>b</mi><mo>≥</mo><mi>a</mi><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"715 ","pages":"Pages 32-45"},"PeriodicalIF":1.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706244","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}
{"title":"A note on joint numerical radius","authors":"Amit Maji , Atanu Manna , Ram Mohapatra","doi":"10.1016/j.laa.2025.03.008","DOIUrl":"10.1016/j.laa.2025.03.008","url":null,"abstract":"<div><div>We investigate the Crawford number and numerical radius of model operators on Hilbert spaces. For an <em>n</em>-tuple of doubly commuting shifts, the joint numerical radius and the joint Crawford number are determined. Additionally, we use the Hermite-Hadamard inequality and the Orlicz function to derive new and improved joint numerical radius inequalities of operators on Hilbert spaces.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"715 ","pages":"Pages 17-31"},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143681502","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}
{"title":"Combinatorial explanation of coefficients of the signless Laplacian characteristic polynomial of a digraph","authors":"Jingyuan Zhang , Xian'an Jin , Weigen Yan","doi":"10.1016/j.laa.2025.03.010","DOIUrl":"10.1016/j.laa.2025.03.010","url":null,"abstract":"<div><div>Let <em>G</em> be a simple digraph with <em>n</em> vertices <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Denote the adjacency matrix and the in-degree matrix of <em>G</em> by <span><math><mi>A</mi><mo>=</mo><msub><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msub></math></span> and <span><math><mi>D</mi><mo>=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mo>(</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><mo>⋯</mo><mo>,</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math></span>, respectively, where <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> if <span><math><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></math></span> is an arc of <em>G</em> and <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> otherwise, and <span><math><msubsup><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> is the number of arcs with head <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> in <em>G</em>. Set <span><math><mi>f</mi><mo>(</mo><mi>G</mi><mo>;</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>det</mi><mo></mo><mo>(</mo><mi>x</mi><msub><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>D</mi><mo>−</mo><mi>A</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></munderover><msup><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>i</mi></mrow></msup><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>i</mi></mrow></msup></math></span>, where <span><math><mi>det</mi><mo></mo><mo>(</mo><mi>X</mi><mo>)</mo></math></span> denotes the determinant of a square matrix <em>X</em>. Then <span><math><mi>f</mi><mo>(</mo><mi>G</mi><mo>;</mo><mi>x</mi><mo>)</mo></math></span> is called the signless Laplacian characteristic polynomial of the digraph <em>G</em>. Li, Lu, Wang and Wang (2023) <span><span>[7]</span></span> gave a combinatorial explanation of <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> of <span><math><mi>f</mi><mo>(</mo><mi>G</mi><mo>;</mo><mi>x</mi><mo>)</mo></math></span>. In this paper, we give combinatorial explanations of all the coefficient","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"717 ","pages":"Pages 56-67"},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808031","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}
{"title":"On the limit points of the smallest positive eigenvalues of graphs","authors":"Sasmita Barik, Debabrota Mondal","doi":"10.1016/j.laa.2025.03.006","DOIUrl":"10.1016/j.laa.2025.03.006","url":null,"abstract":"<div><div>In 1972, Hoffman <span><span>[11]</span></span> initiated the study of limit points of eigenvalues of nonnegative symmetric integer matrices. He posed the question of finding all limit points of the set of spectral radii of all nonnegative symmetric integer matrices. In the same article, the author demonstrated that it is enough to consider the adjacency matrices of simple graphs to study the limit points of spectral radii. Since then, many researchers have worked on similar problems, considering various specific eigenvalues such as the least eigenvalue, the <em>k</em>th largest eigenvalue, and the <em>k</em>th smallest eigenvalue, among others. Motivated by this, we ask the question, “which real numbers are the limit points of the set of the smallest positive eigenvalues (respectively, the largest negative eigenvalues) of graphs?” In this article, we provide a complete answer to this question by proving that any nonnegative (respectively, nonpositive) real number is a limit point of the set of all smallest positive eigenvalues (respectively, largest negative eigenvalues) of graphs. We also show that the union of the sets of limit points of the smallest positive eigenvalues and the largest negative eigenvalues of graphs is dense in <span><math><mi>R</mi></math></span>, the set of all real numbers.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"715 ","pages":"Pages 1-16"},"PeriodicalIF":1.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143681501","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}
{"title":"Unitary similarity and the numerical radius preservers","authors":"Abdellatif Bourhim , Mohamed Mabrouk","doi":"10.1016/j.laa.2025.03.005","DOIUrl":"10.1016/j.laa.2025.03.005","url":null,"abstract":"<div><div>Let <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> be the algebra of all bounded linear operators acting on a separable infinite-dimensional complex Hilbert space <span><math><mi>H</mi></math></span>, and denote by <span><math><mi>w</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> the numerical radius of any operator <span><math><mi>T</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>. In this paper, we describe the form of all bijective linear maps <em>ϕ</em> on <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> for which <span><math><mi>w</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>)</mo><mo>=</mo><mi>w</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>)</mo></math></span> whenever <span><math><mi>T</mi><mo>,</mo><mspace></mspace><mi>S</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> are two unitarily similar operators.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"714 ","pages":"Pages 15-27"},"PeriodicalIF":1.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683388","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}
{"title":"Christensen-Sinclair factorization via semidefinite programming","authors":"Francisco Escudero-Gutiérrez","doi":"10.1016/j.laa.2025.03.007","DOIUrl":"10.1016/j.laa.2025.03.007","url":null,"abstract":"<div><div>We show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert spaces are finite dimensional, is an instance of strong duality of semidefinite programming. This gives an elementary proof of the result and also provides an efficient algorithm to compute the Christensen-Sinclair factorization.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"714 ","pages":"Pages 28-44"},"PeriodicalIF":1.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683389","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}
{"title":"Interval global optimization problem in max-plus algebra","authors":"Helena Myšková, Ján Plavka","doi":"10.1016/j.laa.2025.03.009","DOIUrl":"10.1016/j.laa.2025.03.009","url":null,"abstract":"<div><div>Consider the global optimization problem of minimizing the max-plus product <span><math><mi>A</mi><mo>⊗</mo><mi>x</mi></math></span>, where <em>A</em> is a given matrix and the constraint set is the set of column vectors <em>x</em> such that the sum of products <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>j</mi></mrow></msub><mspace></mspace><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> is equal to <em>c</em> and <em>c</em> is a given positive real constant, <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> are non-negative numbers with sum equal to 1. We show that the solvability of the given global optimization problem is independent of the number <em>c</em> if the components of the vector <em>x</em> can also be negative. From a practical point of view, we further consider the solvability of the global optimization problem with non-negative constraints. We propose an algorithm which decides whether a given problem is solvable, extend the problem to interval matrices and provide an algorithm to verify the solvability of interval global optimization problem.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"714 ","pages":"Pages 45-63"},"PeriodicalIF":1.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683390","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}
Erin C. Carson, Fernando De Terán, Volker Mehrmann, Vanni Noferini, João F. Queiró
{"title":"Preface to the Proceedings of ILAS 2023, Twenty-fifth Conference of the International Linear Algebra Society","authors":"Erin C. Carson, Fernando De Terán, Volker Mehrmann, Vanni Noferini, João F. Queiró","doi":"10.1016/j.laa.2025.03.001","DOIUrl":"10.1016/j.laa.2025.03.001","url":null,"abstract":"","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"721 ","pages":"Pages 1-4"},"PeriodicalIF":1.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170104","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}
{"title":"Isometries of the qubit state space with respect to quantum Wasserstein distances","authors":"Richárd Simon , Dániel Virosztek","doi":"10.1016/j.laa.2025.03.004","DOIUrl":"10.1016/j.laa.2025.03.004","url":null,"abstract":"<div><div>In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence <span><math><msub><mrow><mi>d</mi></mrow><mrow><mtext>sym</mtext></mrow></msub></math></span>, the divergence induced by all of the Pauli matrices. We also give a complete characterization of isometries with respect to <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>, the quantum Wasserstein distance corresponding to the single Pauli matrix <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"714 ","pages":"Pages 1-14"},"PeriodicalIF":1.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683387","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}
{"title":"Minimal rank perturbations of matrix pencils","authors":"Marija Dodig , Marko Stošić","doi":"10.1016/j.laa.2025.03.002","DOIUrl":"10.1016/j.laa.2025.03.002","url":null,"abstract":"<div><div>In this paper we give a solution to the bounded rank perturbation problem for matrix pencils in the case when the rank of the perturbation pencil is the minimal possible. The key ingredient of the paper is a novel, direct link between the bounded rank perturbation problem in the minimal case, and a minimal matrix pencil completion problem.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"721 ","pages":"Pages 81-101"},"PeriodicalIF":1.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169843","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}
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