Linear Algebra and its Applications最新文献

{"title":"On order isomorphisms of locally parallel sets between C⁎-algebras: The case of matrix algebras","authors":"Koki Igarashi ,&nbsp;Jumpei Nakamura ,&nbsp;Saikat Roy ,&nbsp;Ryotaro Tanaka","doi":"10.1016/j.laa.2025.05.018","DOIUrl":"10.1016/j.laa.2025.05.018","url":null,"abstract":"<div><div>We introduce the notion of locally parallel sets of elements of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras which generalizes that of norm attainment sets of continuous functions, and consider a preserver problem on order isomorphisms of locally parallel sets. It is shown that unitary multiplications of Jordan ⁎-isomorphisms give examples of order isomorphisms of locally parallel sets. This is achieved by analyzing the quasi-strong Birkhoff-James orthogonality, a new orthogonality relation between the original Birkhoff-James orthogonality and the strong Birkhoff-James orthogonality. Moreover, it is shown that every order isomorphism of locally parallel sets on the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra of all <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> complex matrices is essentially implemented by two unitary matrices provided that <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 190-219"},"PeriodicalIF":1.0,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144139156","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":"A structure theory for regular graphs with fixed smallest eigenvalue","authors":"Qianqian Yang ,&nbsp;Jack H. Koolen","doi":"10.1016/j.laa.2025.05.013","DOIUrl":"10.1016/j.laa.2025.05.013","url":null,"abstract":"<div><div>In this paper we will give a structure theory for regular graphs with fixed smallest eigenvalue. As a consequence of this theory, we show that a <em>k</em>-regular graph with smallest eigenvalue at least −<em>λ</em> has clique number linear in <em>k</em> if <em>k</em> is large with respect to <em>λ</em>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 114-124"},"PeriodicalIF":1.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106481","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 automorphism group and plain eigenvalues of a graph","authors":"Wei Wang,&nbsp;Xinyue Wang","doi":"10.1016/j.laa.2025.05.011","DOIUrl":"10.1016/j.laa.2025.05.011","url":null,"abstract":"<div><div>We introduce the <em>plain polynomial</em> associated with a graph <em>G</em>, which is defined to be the quotient of the characteristic polynomial and the main polynomial of <em>G</em>. For a graph <em>G</em> with a square-free plain polynomial, we establish an upper bound on the order of its automorphism group in terms of the number of irreducible factors of the plain polynomial over <span><math><mi>Q</mi></math></span>. This improves the previous upper bound using the characteristic polynomial (G. Criscuolo, C.-M. Kwok, A. Mowshowitz, and R. Tortora, The group and the minimal polynomial of a graph, J. Combin. Theory Ser. B 29 (1980) 293–302).</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"722 ","pages":"Pages 154-163"},"PeriodicalIF":1.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134742","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}