Linear Algebra and its Applications最新文献

{"title":"Zero product preserving additive maps on triangular algebras","authors":"Hoger Ghahramani,&nbsp;Neda Ghoreishi,&nbsp;Saber Naseri","doi":"10.1016/j.laa.2025.05.017","DOIUrl":"10.1016/j.laa.2025.05.017","url":null,"abstract":"<div><div>Suppose that <span><math><mi>T</mi><mi>r</mi><mi>i</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> is a unital triangular algebra, where <span><math><mi>M</mi></math></span> is a faithful <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span>-bimodule, and <span><math><mi>U</mi></math></span> is a unital algebra. Let <span><math><mi>θ</mi><mo>:</mo><mi>T</mi><mi>r</mi><mi>i</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>,</mo><mi>B</mi><mo>)</mo><mo>→</mo><mi>U</mi></math></span> be a bijective zero product preserving additive map. We show that under some mild conditions <em>θ</em> is a product of a central invertible element and a ring isomorphism. Our result applies to block upper triangular matrix algebras, nest algebras on Banach spaces and nest subalgebras of von Neumann algebras.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 178-189"},"PeriodicalIF":1.0,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134744","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":"Positive moments forever: Undecidable and decidable cases","authors":"Gemma De les Coves ,&nbsp;Joshua Graf ,&nbsp;Andreas Klingler ,&nbsp;Tim Netzer","doi":"10.1016/j.laa.2025.05.015","DOIUrl":"10.1016/j.laa.2025.05.015","url":null,"abstract":"<div><div>We investigate the generalized moment membership problem for matrices, a formulation equivalent to Skolem's problem for linear recurrence sequences. We show decidability for orthogonal, unitary, and real eigenvalue matrices, and undecidability for matrices over certain commutative and non-commutative polynomial rings. As consequences, we deduce that positivity is decidable for simple unitary linear recurrence sequences and undecidable for linear recurrence sequences over commutative polynomial rings. As a byproduct, we also prove a free version of Pólya's theorem.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 255-275"},"PeriodicalIF":1.0,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138998","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":"The spectral radius of Steiner distance hypermatrices of graphs","authors":"Zhibin Du","doi":"10.1016/j.laa.2025.05.014","DOIUrl":"10.1016/j.laa.2025.05.014","url":null,"abstract":"<div><div>Let <em>G</em> be an <em>n</em>-vertex connected graph with vertex set <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. Given a collection of <em>k</em> vertices (not necessarily distinct, which can be regarded as a tuple), say <span><math><mi>S</mi><mo>∈</mo><mi>V</mi><msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup></math></span>, the Steiner distance <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo></math></span> is defined as the fewest number of edges in any connected subgraph of <em>G</em> containing all the vertices in <em>S</em>. The Steiner distance would be reduced to the classical distance of two vertices in the case of <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>. Accordingly, one can generalize the distance matrix (with <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>) to the order-<em>k</em> hypermatrix, called Steiner distance hypermatrix, in which each entry is the Steiner distance of an <em>n</em>-dimensional array indexed by <em>k</em> vertices (not necessarily distinct). Very recently, Cooper and Tauscheck extended the classical Graham-Pollak theorem from the determinant of distance matrices of trees to the hyperdeterminant of Steiner distance hypermatrices of trees. In this paper, we consider the spectral radius of Steiner distance hypermatrices of general graphs, some extremal results are obtained.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 276-295"},"PeriodicalIF":1.0,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166970","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":"Symmetry in complex unit gain graphs and their spectra","authors":"Pepijn Wissing,&nbsp;Edwin R. van Dam","doi":"10.1016/j.laa.2025.05.012","DOIUrl":"10.1016/j.laa.2025.05.012","url":null,"abstract":"<div><div>Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a construction that transforms an arbitrary complex unit gain graph into infinitely many switching-distinct ones whose spectral symmetry does not imply sign-symmetry. This provides a more general answer to the analogue of an existence question that was recently treated in the context of signed graphs.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 164-177"},"PeriodicalIF":1.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134743","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":"Arbitrarily finely divisible stochastic matrices","authors":"Priyanka Joshi,&nbsp;Helena Šmigoc","doi":"10.1016/j.laa.2025.05.010","DOIUrl":"10.1016/j.laa.2025.05.010","url":null,"abstract":"<div><div>We introduce and study the class of arbitrarily finely divisible stochastic matrices (<span><math><msub><mrow><mi>AFD</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrices): stochastic matrices that have a stochastic <em>c</em>-th root for infinitely many natural numbers <em>c</em>. This notion generalises the class of embeddable stochastic matrices. In particular, if <em>A</em> is a transition matrix for a Markov process over some time period, then arbitrary finely divisibility of <em>A</em> inside the set of stochastic matrices is the necessary and sufficient condition for the existence of a transition matrix corresponding to this Markov process over infinitesimally short periods.</div><div>Our research explores the connection between the spectral properties of an <span><math><msub><mrow><mi>AFD</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrix <em>A</em> and the spectral properties of a limit point <em>L</em> of its stochastic roots. This connection, which is first formalised in the broader context of complex and real square matrices, poses restrictions on <em>A</em> assuming <em>L</em> is given. For example, if an <span><math><msub><mrow><mi>AFD</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrix <em>A</em> has a corresponding irreducible limit point <em>L</em>, then <em>A</em> has to be a circulant matrix. We identify all matrices that can be a limit point of stochastic roots for some non-singular <span><math><msub><mrow><mi>AFD</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrix. Further, we demonstrate a construction of a class of <span><math><msub><mrow><mi>AFD</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrices with a given limit point <em>L</em> from embeddable matrices. To illustrate these theoretical findings, we examine specific cases, including <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrices, <span><math><mn>3</mn><mo>×</mo><mn>3</mn></math></span> circulant matrices, and offer a complete characterisation of <span><math><msub><mrow><mi>AFD</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrices of rank-two.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 125-153"},"PeriodicalIF":1.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116178","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":"Optimization flow for approximating a matrix state involving orthonormal constraints","authors":"Bing-Ze Lu ,&nbsp;Matthew M. Lin ,&nbsp;Yu-Chen Shu","doi":"10.1016/j.laa.2025.05.009","DOIUrl":"10.1016/j.laa.2025.05.009","url":null,"abstract":"<div><div>In this work, we introduce a continuous-time dynamical flow. The purpose of this flow is to approximate a matrix state while precisely adhering to orthonormal constraints. Additionally, we apply restrictions on the probability distribution that expand beyond these constraints. Our work contributes in two ways. Firstly, we demonstrate in theory that our proposed flow guarantees convergence to the stationary point of the objective function. It consistently reduces the value of this function for almost any initial value. Secondly, we show that our approach can retrieve the decomposition of a given matrix. Even if the matrix is not inherently decomposable, our results illustrate that our approach remains reliable in obtaining optimal solutions.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 220-236"},"PeriodicalIF":1.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138997","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":"New families of trees determined by their spectra","authors":"Zhibin Du ,&nbsp;Carlos M. da Fonseca","doi":"10.1016/j.laa.2025.05.007","DOIUrl":"10.1016/j.laa.2025.05.007","url":null,"abstract":"<div><div>In a groundbreaking work, Rowlinson in 2010 established some bounds for the multiplicities of an eigenvalue of a tree. These limits were obtained using the star complement technique and have been the subject of increasing interest in recent years. In this paper, we refine them and as a consequence we obtain new families of trees determined by their spectra. For this purpose, we develop a new method based on the eigenvalue multiplicities. As special cases, we can recover the spectral characterization recently obtained for the <em>p</em>-sun and the double <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-sun.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 101-113"},"PeriodicalIF":1.0,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144099653","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":"Quasi-immanants","authors":"John M. Campbell","doi":"10.1016/j.laa.2025.04.029","DOIUrl":"10.1016/j.laa.2025.04.029","url":null,"abstract":"<div><div>For an integer partition <em>λ</em> of <em>n</em> and an <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrix <em>A</em>, consider the expansion of the immanant <span><math><msup><mrow><mtext>Imm</mtext></mrow><mrow><mi>λ</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> as a sum indexed by permutations <em>σ</em> of order <em>n</em>, with coefficients given by the irreducible characters <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mi>λ</mi></mrow></msup><mo>(</mo><mtext>ctype</mtext><mo>(</mo><mi>σ</mi><mo>)</mo><mo>)</mo></math></span> of the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, for the cycle type <span><math><mtext>ctype</mtext><mo>(</mo><mi>σ</mi><mo>)</mo><mo>⊢</mo><mi>n</mi></math></span> of <em>σ</em>. Skandera et al. have introduced combinatorial interpretations of a generalization of immanants given by replacing the coefficient <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mi>λ</mi></mrow></msup><mo>(</mo><mtext>ctype</mtext><mo>(</mo><mi>σ</mi><mo>)</mo><mo>)</mo></math></span> with preimages with respect to the Frobenius morphism of elements among the distinguished bases of the algebra <span><math><mtext>Sym</mtext></math></span> of symmetric functions. Since <span><math><mtext>Sym</mtext></math></span> is contained in the algebra <span><math><mtext>QSym</mtext></math></span> of quasisymmetric functions, this leads us to further generalize immanants with the use of quasisymmetric functions. Since bases of <span><math><mtext>QSym</mtext></math></span> are indexed by integer compositions, we make use of cycle compositions in place of cycle types to define the family of <em>quasi-immanants</em> introduced in this paper. This is achieved through the use of the quasisymmetric power sum bases due to Ballantine et al., and we prove a combinatorial formula for the coefficients arising in an analogue, given by a special case of quasi-immanants associated with quasisymmetric Schur functions, of second immanants.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 67-80"},"PeriodicalIF":1.0,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084335","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":"Generalized Grassmann graphs of orthogonal decompositions of Hilbert spaces","authors":"Bojan Kuzma ,&nbsp;Mark Pankov","doi":"10.1016/j.laa.2025.05.006","DOIUrl":"10.1016/j.laa.2025.05.006","url":null,"abstract":"<div><div>Classical Chow's theorem describes automorphisms of Grassmann graphs. We consider generalized Grassmann and ortho-Grassmann graphs whose vertices are countable orthogonal decompositions of a complex Hilbert space into subspaces of prescribed dimensions. The two main results concern automorphisms of these graphs.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"720 ","pages":"Pages 303-338"},"PeriodicalIF":1.0,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069465","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 ranges are shadows","authors":"Alan Wiggins ,&nbsp;Edwin Xie","doi":"10.1016/j.laa.2025.05.005","DOIUrl":"10.1016/j.laa.2025.05.005","url":null,"abstract":"<div><div>We present a new perspective on the numerical range of <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices as varying “shadows” of an embedding of <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>. This framework gives us geometric proofs of the elliptic range theorem and the Toeplitz-Hausdorff theorem. We apply this perspective to the Berezin Range or linear operators on finite-dimensional supbspaces of the Hardy-Hilbert space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>D</mi><mo>)</mo></math></span> of the open unit disk <span><math><mi>D</mi></math></span>. We characterize the convexity of the Berezin range for two-dimensional subspaces and show that uncountably many unitary conjugates of a given operator are needed to “cover” the numerical range using Berezin ranges if the boundary of the numerical range is not smooth.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 81-100"},"PeriodicalIF":1.0,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144088676","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}