Pub Date : 2026-01-05DOI: 10.1016/j.laa.2025.12.019
Ming-Cheng Tsai , Huajun Huang
We characterize maps , and , that have the multiplicative spectrum or trace preserving property: where is the set of doubly stochastic, row stochastic, or column stochastic matrices, or the space spanned by one of these sets. Linearity is assumed when . We show that every stochastic matrix contains a real doubly stochastic component that carries the spectral information. In consequence, the multiplicative spectrum or trace preservers on these sets are linked to the corresponding preservers on the space of doubly stochastic matrices. Moreover, when , multiplicative trace preservers always coincide with multiplicative spectrum preservers.
{"title":"Multiplicative trace and spectrum preservers on stochastic matrices","authors":"Ming-Cheng Tsai , Huajun Huang","doi":"10.1016/j.laa.2025.12.019","DOIUrl":"10.1016/j.laa.2025.12.019","url":null,"abstract":"<div><div>We characterize maps <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>:</mo><mi>S</mi><mo>→</mo><mi>S</mi></math></span>, <span><math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>m</mi></math></span> and <span><math><mi>m</mi><mo>≥</mo><mn>1</mn></math></span>, that have the multiplicative spectrum or trace preserving property:<span><span><span><math><mi>spec</mi><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>⋯</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>=</mo><mi>spec</mi><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>,</mo><mspace></mspace><mtext>or</mtext><mspace></mspace><mi>tr</mi><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>⋯</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>=</mo><mi>tr</mi><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>,</mo></math></span></span></span> where <span><math><mi>S</mi></math></span> is the set of <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> doubly stochastic, row stochastic, or column stochastic matrices, or the space spanned by one of these sets. Linearity is assumed when <span><math><mi>m</mi><mo>=</mo><mn>1</mn></math></span>. We show that every stochastic matrix contains a real doubly stochastic component that carries the spectral information. In consequence, the multiplicative spectrum or trace preservers on these sets <span><math><mi>S</mi></math></span> are linked to the corresponding preservers on the space of doubly stochastic matrices. Moreover, when <span><math><mi>m</mi><mo>≥</mo><mn>3</mn></math></span>, multiplicative trace preservers always coincide with multiplicative spectrum preservers.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 118-151"},"PeriodicalIF":1.1,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979681","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}
Pub Date : 2026-01-02DOI: 10.1016/j.laa.2025.12.023
Prem Dagar, Mahendra Kumar Verma
Let F be a non-Archimedean local field and be its ring of integers with ϖ chosen as a fixed generator for the maximal ideal of . Define as the finite local ring. In this paper, we describe the explicit construction of parabolically induced representations of the group for and establish an irreducibility criterion for these representations. Additionally, we determine the number of irreducible constituents in the case of reducibility. Furthermore, we study the primitive cuspidal representations and explore the representations of using the Whittaker and Kirillov model.
设F是一个非阿基米德局部域，O是它的整数环，其中选择π作为O的最大理想的固定发生器。定义O n:=O/ < O n >作为有限局部环。本文给出了群GL2(O)对l >；1的抛物诱导表示的显式构造，并建立了这些表示的不可约准则。此外，我们确定在可还原性的情况下不可还原性成分的数量。此外，我们研究了原始的反转表示，并利用Whittaker和Kirillov模型探索了GL2(O)的表示。
{"title":"On representations of GL2 over finite chain rings","authors":"Prem Dagar, Mahendra Kumar Verma","doi":"10.1016/j.laa.2025.12.023","DOIUrl":"10.1016/j.laa.2025.12.023","url":null,"abstract":"<div><div>Let F be a non-Archimedean local field and <span><math><mi>O</mi></math></span> be its ring of integers with <em>ϖ</em> chosen as a fixed generator for the maximal ideal of <span><math><mi>O</mi></math></span>. Define <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mo>:</mo><mo>=</mo><mi>O</mi><mo>/</mo><mo>〈</mo><msup><mrow><mi>ϖ</mi></mrow><mrow><mi>ℓ</mi></mrow></msup><mo>〉</mo></math></span> as the finite local ring. In this paper, we describe the explicit construction of parabolically induced representations of the group <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mo>)</mo></math></span> for <span><math><mi>ℓ</mi><mo>></mo><mn>1</mn></math></span> and establish an irreducibility criterion for these representations. Additionally, we determine the number of irreducible constituents in the case of reducibility. Furthermore, we study the primitive cuspidal representations and explore the representations of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mo>)</mo></math></span> using the Whittaker and Kirillov model.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 73-88"},"PeriodicalIF":1.1,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928392","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}
Pub Date : 2026-01-02DOI: 10.1016/j.laa.2025.12.021
Emily J. King , Dustin G. Mixon , Shayne Waldron
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary group or general linear group. If isomorphism also allows permutations of the subspaces, then the problem is at least as hard as graph isomorphism. Otherwise, we provide a variety of polynomial-time algorithms with Matlab implementations to test for isomorphism.
{"title":"Testing isomorphism between tuples of subspaces","authors":"Emily J. King , Dustin G. Mixon , Shayne Waldron","doi":"10.1016/j.laa.2025.12.021","DOIUrl":"10.1016/j.laa.2025.12.021","url":null,"abstract":"<div><div>Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary group or general linear group. If isomorphism also allows permutations of the subspaces, then the problem is at least as hard as graph isomorphism. Otherwise, we provide a variety of polynomial-time algorithms with Matlab implementations to test for isomorphism.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 50-72"},"PeriodicalIF":1.1,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928391","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}
Pub Date : 2026-01-02DOI: 10.1016/j.laa.2025.12.022
Chenyue Feng, Shoumin Liu , Xumin Wang
In this paper, we will compute the characteristic polynomials for finite dimensional representations of classical complex Lie algebras and the exceptional Lie algebra of type , which can be obtained through the orbits of integral weights under the action of their corresponding Weyl groups and the invariant polynomial theory of the Weyl groups. We show that the characteristic polynomials can be decomposed into products of irreducible orbit factors, each of which is invariant under the action of their corresponding Weyl groups.
{"title":"Characteristic polynomials for classical Lie algebras and their orbit decompositions","authors":"Chenyue Feng, Shoumin Liu , Xumin Wang","doi":"10.1016/j.laa.2025.12.022","DOIUrl":"10.1016/j.laa.2025.12.022","url":null,"abstract":"<div><div>In this paper, we will compute the characteristic polynomials for finite dimensional representations of classical complex Lie algebras and the exceptional Lie algebra of type <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, which can be obtained through the orbits of integral weights under the action of their corresponding Weyl groups and the invariant polynomial theory of the Weyl groups. We show that the characteristic polynomials can be decomposed into products of irreducible orbit factors, each of which is invariant under the action of their corresponding Weyl groups.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 28-49"},"PeriodicalIF":1.1,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928390","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}
Pub Date : 2025-12-31DOI: 10.1016/j.laa.2025.12.017
Wojciech Młotkowski , Marek Skrzypczyk , Michał Wojtylak
We compute the quadratic embedding constant for complete bipartite graphs with disjoint edges removed. Moreover, we study the quadratic embedding property for theta graphs, i.e., graphs consisting of three paths with common initial points and common endpoints. As a result, we provide an infinite family of primary graphs that are not quadratically embeddable.
{"title":"On quadratic embeddability of bipartite graphs and theta graphs","authors":"Wojciech Młotkowski , Marek Skrzypczyk , Michał Wojtylak","doi":"10.1016/j.laa.2025.12.017","DOIUrl":"10.1016/j.laa.2025.12.017","url":null,"abstract":"<div><div>We compute the quadratic embedding constant for complete bipartite graphs with disjoint edges removed. Moreover, we study the quadratic embedding property for theta graphs, i.e., graphs consisting of three paths with common initial points and common endpoints. As a result, we provide an infinite family of primary graphs that are not quadratically embeddable.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 89-115"},"PeriodicalIF":1.1,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928393","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}
Pub Date : 2025-12-30DOI: 10.1016/j.laa.2025.12.018
Shankhadeep Mondal, Ram Narayan Mohapatra
This paper investigates the optimization of dual frame pairs in the context of erasure problems in data transmission, using a graph theoretical approach. Frames are essential for mitigating errors and signal loss due to their redundancy properties. We address the use of spectral radius and operator norm for error measurements, presenting conditions for the optimality of dual pairs for one and two erasures. Our study shows that a tight frame generated by connected graphs and its canonical dual pair is optimal for one-erasure scenarios. Additionally, we compute the spectral radius of the error operator for one and two erasures in graph-generated frames, establishing necessary conditions for dual pair optimality.
{"title":"Optimal dual frame pairs: A synergy with graph theory","authors":"Shankhadeep Mondal, Ram Narayan Mohapatra","doi":"10.1016/j.laa.2025.12.018","DOIUrl":"10.1016/j.laa.2025.12.018","url":null,"abstract":"<div><div>This paper investigates the optimization of dual frame pairs in the context of erasure problems in data transmission, using a graph theoretical approach. Frames are essential for mitigating errors and signal loss due to their redundancy properties. We address the use of spectral radius and operator norm for error measurements, presenting conditions for the optimality of dual pairs for one and two erasures. Our study shows that a tight frame generated by connected graphs and its canonical dual pair is optimal for one-erasure scenarios. Additionally, we compute the spectral radius of the error operator for one and two erasures in graph-generated frames, establishing necessary conditions for dual pair optimality.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 1-27"},"PeriodicalIF":1.1,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145895934","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}
Pub Date : 2025-12-23DOI: 10.1016/j.laa.2025.12.016
Daniel Vitas
The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial f in the matrix algebra is a vector space for every . We prove this conjecture for the case where f has degree 3 and K is an algebraically closed field of characteristic 0.
{"title":"The L'vov-Kaplansky conjecture for polynomials of degree three","authors":"Daniel Vitas","doi":"10.1016/j.laa.2025.12.016","DOIUrl":"10.1016/j.laa.2025.12.016","url":null,"abstract":"<div><div>The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial <em>f</em> in the matrix algebra <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>K</mi><mo>)</mo></math></span> is a vector space for every <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. We prove this conjecture for the case where <em>f</em> has degree 3 and <em>K</em> is an algebraically closed field of characteristic 0.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"733 ","pages":"Pages 205-232"},"PeriodicalIF":1.1,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880820","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}
Pub Date : 2025-12-19DOI: 10.1016/j.laa.2025.12.014
David Aleja , Julio Flores , Eva Primo , Daniel Rodríguez , Miguel Romance
In this paper we analyze PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of the PageRank of a graph is given in terms of the number and nature of its strongly connected components. The method presented essentially follows the classic Power's Method by means of a feedback-PageRank that allows to precisely compute the fixed points, in terms of the (left-hand) Perron vector of each strongly connected component.
{"title":"Fixed points of personalized PageRank centrality: From irreducible to reducible networks","authors":"David Aleja , Julio Flores , Eva Primo , Daniel Rodríguez , Miguel Romance","doi":"10.1016/j.laa.2025.12.014","DOIUrl":"10.1016/j.laa.2025.12.014","url":null,"abstract":"<div><div>In this paper we analyze PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of the PageRank of a graph is given in terms of the number and nature of its strongly connected components. The method presented essentially follows the classic <em>Power's Method</em> by means of a <em>feedback-PageRank</em> that allows to precisely compute the fixed points, in terms of the (left-hand) Perron vector of each strongly connected component.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"733 ","pages":"Pages 233-272"},"PeriodicalIF":1.1,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880818","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}
Pub Date : 2025-12-17DOI: 10.1016/j.laa.2025.12.009
Beata Derȩgowska , Simon Foucart , Barbara Lewandowska
It is shown in this note that one can decide whether an n-dimensional subspace of is isometrically isomorphic to by testing a finite number of determinental inequalities. As a byproduct, an elementary proof is provided for the fact that an n-dimensional subspace of with projection constant equal to one must be isometrically isomorphic to .
{"title":"When is a subspace of ℓ∞N isometrically isomorphic to ℓ∞n?","authors":"Beata Derȩgowska , Simon Foucart , Barbara Lewandowska","doi":"10.1016/j.laa.2025.12.009","DOIUrl":"10.1016/j.laa.2025.12.009","url":null,"abstract":"<div><div>It is shown in this note that one can decide whether an <em>n</em>-dimensional subspace of <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>N</mi></mrow></msubsup></math></span> is isometrically isomorphic to <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> by testing a finite number of determinental inequalities. As a byproduct, an elementary proof is provided for the fact that an <em>n</em>-dimensional subspace of <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>N</mi></mrow></msubsup></math></span> with projection constant equal to one must be isometrically isomorphic to <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"733 ","pages":"Pages 171-177"},"PeriodicalIF":1.1,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145788849","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}
Pub Date : 2025-12-16DOI: 10.1016/j.laa.2025.12.012
Bohui Ban , Xuzhou Zhan , Yongjian Hu
This paper presents a complete description of the set consisting of all allowable McMillan degrees of a nonzero Toeplitz matrix (not necessarily square) and an explicit formula for the rational generating functions of such matrices with a prescribed allowable McMillan degree. This analysis extends the earlier work by Heinig and Rost concerning the rational generating functions of a nonsingular Toeplitz matrix.
{"title":"On the rational generating functions of Toeplitz matrices","authors":"Bohui Ban , Xuzhou Zhan , Yongjian Hu","doi":"10.1016/j.laa.2025.12.012","DOIUrl":"10.1016/j.laa.2025.12.012","url":null,"abstract":"<div><div>This paper presents a complete description of the set consisting of all allowable McMillan degrees of a nonzero Toeplitz matrix (not necessarily square) and an explicit formula for the rational generating functions of such matrices with a prescribed allowable McMillan degree. This analysis extends the earlier work by Heinig and Rost concerning the rational generating functions of a nonsingular Toeplitz matrix.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"733 ","pages":"Pages 155-170"},"PeriodicalIF":1.1,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145788848","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号