Linear Algebra and its Applications最新文献

{"title":"A spectral analogue of Ore's problem on Turán theorem","authors":"Lele Liu ,&nbsp;Bo Ning","doi":"10.1016/j.laa.2026.01.012","DOIUrl":"10.1016/j.laa.2026.01.012","url":null,"abstract":"<div><div>We establish a spectral counterpart to Ore's problem (1962) which asks for the maximum size of an <em>n</em>-vertex graph such that its complement is connected and does not contain <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> as a subgraph, where <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> is a clique of order <span><math><mi>r</mi><mo>+</mo><mn>1</mn></math></span>. Specifically, we characterize the unique graph achieving the maximum spectral radius among all <em>n</em>-vertex, <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span>-free graphs with connected complements. The proof strategy combines the association of the extremal graph with an auxiliary tree to infer its structure and technical spectral analysis of the extremal graphs' Perron vector.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"735 ","pages":"Pages 112-122"},"PeriodicalIF":1.1,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036316","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":"Commuting graphs of p-adic matrices","authors":"Ralph Morrison","doi":"10.1016/j.laa.2026.01.008","DOIUrl":"10.1016/j.laa.2026.01.008","url":null,"abstract":"<div><div>We study the commuting graph of <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices over the field of <em>p</em>-adics <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, whose vertices are non-scalar <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices with entries in <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and whose edges connect pairs of matrices that commute under matrix multiplication. We prove that this graph is connected if and only if <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, with <em>n</em> neither prime nor a power of <em>p</em>. We also prove that in the case of <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mi>q</mi></math></span> for <em>q</em> a prime with <span><math><mi>q</mi><mo>≥</mo><mn>7</mn></math></span>, the commuting graph has the maximum possible diameter of 6; these are the first known such examples independent of the axiom of choice. We also find choices of <em>p</em> and <em>n</em> yielding diameter 4 and diameter 5 commuting graphs, and prove general bounds depending on <em>p</em> and <em>n</em>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"735 ","pages":"Pages 188-202"},"PeriodicalIF":1.1,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036317","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":"Log-majorizations between quasi-geometric type means for matrices","authors":"Fumio Hiai","doi":"10.1016/j.laa.2026.01.003","DOIUrl":"10.1016/j.laa.2026.01.003","url":null,"abstract":"<div><div>In this paper, for <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>∖</mo><mo>{</mo><mn>1</mn><mo>}</mo></math></span>, <span><math><mi>p</mi><mo>&gt;</mo><mn>0</mn></math></span> and positive semidefinite matrices <em>A</em> and <em>B</em>, we consider the quasi-extensions <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>p</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo><mo>:</mo><mo>=</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>α</mi></mrow></msub><msup><mrow><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><msup><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup></math></span> of several <em>α</em>-weighted geometric type matrix means <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> such as the <em>α</em>-weighted geometric mean in Kubo–Ando's sense, the Rényi mean, etc. The log-majorization <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>p</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo><msub><mrow><mo>≺</mo></mrow><mrow><mi>log</mi></mrow></msub><msub><mrow><mi>N</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>q</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> is examined for pairs <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span> of those <em>α</em>-weighted geometric type means. The joint concavity/convexity of the trace functions <span><math><mrow><mi>Tr</mi></mrow><mspace></mspace><msub><mrow><mi>M</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>p</mi></mrow></msub></math></span> is also discussed based on theory of quantum divergences.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"735 ","pages":"Pages 123-174"},"PeriodicalIF":1.1,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036321","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":"Derived equivalences between defective rectangles","authors":"Qiang Dong ,&nbsp;Shunye Li","doi":"10.1016/j.laa.2026.01.019","DOIUrl":"10.1016/j.laa.2026.01.019","url":null,"abstract":"<div><div>In this article, we present quiver realizations of two classes of algebras that are derived equivalent to upper triangular matrix algebras. We investigate defective rectangle algebras and show that four of them are derived equivalent. Moreover, we establish derived equivalences between certain defective rectangle algebras and Nakayama algebras.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"735 ","pages":"Pages 287-306"},"PeriodicalIF":1.1,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036323","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":"Numerical radius and ℓp operator norm of Kronecker products and Schur powers: inequalities and equalities","authors":"Pintu Bhunia ,&nbsp;Sujit Sakharam Damase ,&nbsp;Apoorva Khare","doi":"10.1016/j.laa.2026.01.005","DOIUrl":"10.1016/j.laa.2026.01.005","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Suppose &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a complex &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; matrix and &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a bounded linear operator on a complex Hilbert space &lt;span&gt;&lt;math&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We show that &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; denotes the numerical radius and &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. This refines Holbrook's classical bound &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; (1969) &lt;span&gt;&lt;span&gt;[31]&lt;/span&gt;&lt;/span&gt;, when all entries of &lt;em&gt;A&lt;/em&gt; are non-negative. If moreover &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; ∀&lt;em&gt;i&lt;/em&gt;, we prove that &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; if and only if &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. We then extend these and other results to the more general setting of semi-Hilbertian spaces induced by a positive operator.&lt;/div&gt;&lt;div&gt;In the reverse direction, we also specialize these results to Kronecker products and hence to Schur/entrywise products, of matrices: (1)(a) We first provide an alternate proof (using &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;) of a result of Goldberg and Zwas (1974) &lt;span&gt;&lt;span&gt;[24]&lt;/span&gt;&lt;/span&gt; that if the spectral norm of &lt;em&gt;A&lt;/em&gt; equals its spectral radius, then each Jordan block for each maximum-modulus eigenvalue must be &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; (“partial diagonalizability”). (b) Using our approach, we further show given &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; that &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"735 ","pages":"Pages 1-30"},"PeriodicalIF":1.1,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969253","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":"Spectral radius and rainbow k-factors of graphs","authors":"Liwen Zhang,&nbsp;Zhiyuan Zhang","doi":"10.1016/j.laa.2026.01.022","DOIUrl":"10.1016/j.laa.2026.01.022","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>G</mi></mrow><mrow><mfrac><mrow><mi>k</mi><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub><mo>}</mo></math></span> be a set of graphs on the same vertex set <span><math><mi>V</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></math></span> where <span><math><mi>k</mi><mo>⋅</mo><mi>n</mi></math></span> is even. We say <span><math><mi>G</mi></math></span> admits a rainbow <em>k</em>-factor if there exists a <em>k</em>-regular graph <em>F</em> on the vertex set <em>V</em> such that all edges of <em>F</em> are from different members of <span><math><mi>G</mi></math></span>. In this paper, we show a sufficient spectral condition for the existence of a rainbow <em>k</em>-factor for <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>, which is that if <span><math><mi>ρ</mi><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>≥</mo><mi>ρ</mi><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>∨</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∪</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub><mo>)</mo><mo>)</mo></math></span> for each <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mi>G</mi></math></span>, then <span><math><mi>G</mi></math></span> admits a rainbow <em>k</em>-factor unless <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mo>⋯</mo><mo>=</mo><msub><mrow><mi>G</mi></mrow><mrow><mfrac><mrow><mi>k</mi><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub><mo>≅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>∨</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∪</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"735 ","pages":"Pages 307-318"},"PeriodicalIF":1.1,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090724","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 representations of GL2 over finite chain rings","authors":"Prem Dagar,&nbsp;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>&gt;</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":"2026-04-01","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}

{"title":"Tangent Lie algebras of automorphism groups of free algebras","authors":"Ivan Shestakov ,&nbsp;Ualbai Umirbaev","doi":"10.1016/j.laa.2025.12.020","DOIUrl":"10.1016/j.laa.2025.12.020","url":null,"abstract":"<div><div>We study an analogue of the Andreadakis–Johnson filtration for automorphism groups of free algebras and introduce the notion of tangent Lie algebras for certain automorphism groups, defined as subalgebras of the Lie algebra of derivations. We show that, for many classical varieties of algebras, the tangent Lie algebra is contained in the Lie algebra of derivations with constant divergence. We also introduce the concepts of approximately tame and absolutely wild automorphisms of free algebras in arbitrary varieties and employ tangent Lie algebras to investigate their properties. It is shown that nearly all known examples of wild automorphisms of free algebras are absolutely wild, with the notable exceptions of the Nagata and Anick automorphisms. We show that the Bergman automorphism of free matrix algebras of order two is absolutely wild. Furthermore, we prove that free algebras in any variety of polynilpotent Lie algebras–except for the abelian and metabelian varieties–also possess absolutely wild automorphisms.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"734 ","pages":"Pages 193-223"},"PeriodicalIF":1.1,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979684","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":"Multiplicative trace and spectrum preservers on stochastic matrices","authors":"Ming-Cheng Tsai ,&nbsp;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":"2026-04-01","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}

{"title":"Testing isomorphism between tuples of subspaces","authors":"Emily J. King ,&nbsp;Dustin G. Mixon ,&nbsp;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":"2026-04-01","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}