Linear Algebra and its Applications最新文献

{"title":"Group gradings on finite-dimensional incidence algebras. II","authors":"Helen Samara Dos Santos ,&nbsp;Felipe Yukihide Yasumura","doi":"10.1016/j.laa.2025.07.027","DOIUrl":"10.1016/j.laa.2025.07.027","url":null,"abstract":"<div><div>We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 273-290"},"PeriodicalIF":1.1,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766595","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":"Majorizations for probability distributions, column stochastic matrices and their linear preservers","authors":"Pavel Shteyner","doi":"10.1016/j.laa.2025.07.024","DOIUrl":"10.1016/j.laa.2025.07.024","url":null,"abstract":"<div><div>In this paper, we study majorization for probability distributions and column stochastic matrices. We show that majorizations in general can be reduced to the aforementioned sets. We characterize linear operators that preserve majorization for probability distributions, and show their equivalence to operators preserving vector majorization. Our main result provides a complete characterization of linear preservers of strong majorization for column stochastic matrices, revealing a richer structure of preservers than in the standard setting. As a prerequisite to this characterization, we solve the problem of characterizing linear preservers of majorization for zero-sum vectors, which yields a new structural insight into the classical results of Ando and of Li and Poon.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 291-327"},"PeriodicalIF":1.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766596","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 weighted spectral geometric mean and quantum divergence","authors":"Miran Jeong ,&nbsp;Sejong Kim ,&nbsp;Tin-Yau Tam","doi":"10.1016/j.laa.2025.07.025","DOIUrl":"10.1016/j.laa.2025.07.025","url":null,"abstract":"<div><div>A new class of weighted spectral geometric means has recently been introduced. In this paper, we present its inequalities in terms of the Löwner order, operator norm, and trace. Moreover, we establish a log-majorization relationship between the new spectral geometric mean and the Rényi relative operator entropy. We also study the quantum divergence of the quantity, given by the difference of trace values between the arithmetic mean and new spectral geometric mean. Finally, we study the barycenter that minimizes the weighted sum of quantum divergences for given variables.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 164-179"},"PeriodicalIF":1.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750354","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":"Doubly transitive equiangular tight frames that contain regular simplices","authors":"Matthew Fickus,&nbsp;Evan C. Lake","doi":"10.1016/j.laa.2025.07.023","DOIUrl":"10.1016/j.laa.2025.07.023","url":null,"abstract":"<div><div>An equiangular tight frame (ETF) is a finite sequence of equal norm vectors in a Hilbert space that achieves equality in the Welch bound, and so has minimal coherence. The binder of an ETF is the set of all subsets of its indices whose corresponding vectors form a regular simplex. An ETF achieves equality in Donoho and Elad's spark bound if and only if its binder is nonempty. When this occurs, its binder is the set of all linearly dependent subsets of it of minimal size. Moreover, if members of the binder form a balanced incomplete block design (BIBD) then its incidence matrix can be phased to produce a sparse representation of its dual (Naimark complement). A few infinite families of ETFs are known to have this remarkable property. In this paper, we relate this property to the recently introduced concept of a doubly transitive equiangular tight frame (DTETF), namely an ETF for which the natural action of its symmetry group is doubly transitive. In particular, we show that the binder of any DTETF is either empty or forms a BIBD, and moreover that when the latter occurs, any member of the binder of its dual is an oval of this BIBD. We then apply this general theory to certain known infinite families of DTETFs. Specifically, any symplectic form on a finite vector space yields a DTETF, and we compute the binder of it and its dual, showing that the former is empty except in a single notable case, and that the latter consists of affine Lagrangian subspaces. This unifies and generalizes several results from the existing literature. We then consider the binders of four infinite families of DTETFs that arise from quadratic forms over the field of two elements, showing that two of these are empty except in a finite number of cases, whereas the other two form BIBDs that relate to each other, and to Lagrangian subspaces, in nonobvious ways.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 113-163"},"PeriodicalIF":1.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738686","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 Tsallis relative entropies and their preservers on positive cones in operator algebras and in matrix algebras","authors":"Lei Li ,&nbsp;Lajos Molnár ,&nbsp;Xueyan Yang","doi":"10.1016/j.laa.2025.07.026","DOIUrl":"10.1016/j.laa.2025.07.026","url":null,"abstract":"<div><div>In this paper, we are mainly concerned with Tsallis relative entropies and Tsallis operator relative entropies on positive cones in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras but also consider their limit cases, the Umegaki relative entropy and the relative operator entropy. Motivated by Wigner's result on quantum mechanical symmetry transformations, we describe the surjective transformations on positive cones that preserve any of the corresponding numerical relative entropies. In the case of matrix algebras, we present related results where the surjectivity assumption is dropped. We will see that, although the numerical quantities under consideration do not suggest any sort of linearity, their preservers are intimately connected to the most fundamental linear and algebraic isomorphisms of the underlying full algebras.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 244-272"},"PeriodicalIF":1.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766594","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 an infinite family of integral and distance integral Cayley graphs with few distance eigenvalues","authors":"Daniele D'Angeli,&nbsp;Alfredo Donno,&nbsp;Stefano Spessato","doi":"10.1016/j.laa.2025.07.022","DOIUrl":"10.1016/j.laa.2025.07.022","url":null,"abstract":"<div><div>We construct the distance matrices of the Cayley graphs of the Pauli groups, recursively defined by using the notion of central product of groups, with respect to a suitable symmetric generating set. These Cayley graphs constitute an infinite sequence <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></msub></math></span> of regular non distance-regular graphs of degree <span><math><mn>3</mn><mi>n</mi><mo>+</mo><mn>2</mn></math></span> with integral adjacency spectrum. We explicitly determine all the distance eigenvectors and eigenvalues, showing that each of these graphs has exactly six distinct distance eigenvalues, answering a question by Atik and Panigrahi. Moreover, all the distance eigenvalues have the remarkable property of being integers. We compute the diameter of each graph and the cardinality of all spheres centered at any vertex. We are also able to determine topological indices like the Wiener index, the Wiener polarity index, the Harary index, as well as the distance energy. We finally show that this sequence of Cayley graphs is a counterexample to two conjectures formulated by Aouchiche and Hansen.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 180-215"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750355","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":"Embedding matrix algebras into ultragraph Leavitt path algebras and applications","authors":"Romar B. Dinoy ,&nbsp;Tran Giang Nam ,&nbsp;Jocelyn P. Vilela","doi":"10.1016/j.laa.2025.07.021","DOIUrl":"10.1016/j.laa.2025.07.021","url":null,"abstract":"<div><div>In this article, we provide criteria for an ultragraph <span><math><mi>G</mi></math></span> so that for any field <em>K</em> and <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, the full 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 embedded in the associated Leavitt path algebra of <span><math><mi>G</mi></math></span>. This result, which has not appeared in the context of Leavitt path algebras of graphs, is then applied to characterize properties of Lie solvable and Lie nilpotent ultragraph Leavitt path algebras, and compute the solvable index of a Lie solvable ultragraph Leavitt path algebra.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 216-243"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750356","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":"Zero-dilation indices and numerical ranges","authors":"Kennett L. Dela Rosa","doi":"10.1016/j.laa.2025.07.018","DOIUrl":"10.1016/j.laa.2025.07.018","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The zero-dilation index &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&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 matrix &lt;em&gt;A&lt;/em&gt; is the largest integer &lt;em&gt;k&lt;/em&gt; for which &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is unitarily similar to &lt;em&gt;A&lt;/em&gt;. In this study, the zero-dilation indices of certain block matrices are considered, namely, the block matrix analogues of companion matrices and upper triangular KMS matrices, respectively shown as&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&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;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;⨁&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&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;/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;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;and&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;K&lt;/mi&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;mi&gt;A&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋯&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋱&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋮&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋱&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;⋮&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋮&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋮&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋱&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;⋯&lt;/mo&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;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are &lt;em&gt;mn&lt;/em&gt;-by-&lt;em&gt;mn&lt;/em&gt; and &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;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are &lt;em&gt;n&lt;/em&gt;-by-&lt;em&gt;n&lt;/em&gt;. Provided &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;⨁&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&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;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is nonsingular, it is proved that &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&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; satisfies the following: if &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is odd (respectively, &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is even), then &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/m","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 91-112"},"PeriodicalIF":1.0,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702568","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":"Close to optimal column approximation using a single SVD","authors":"A.I. Osinsky","doi":"10.1016/j.laa.2025.07.016","DOIUrl":"10.1016/j.laa.2025.07.016","url":null,"abstract":"<div><div>The best column approximation in the Frobenius norm with <em>r</em> columns has an error at most <span><math><msqrt><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msqrt></math></span> times larger than the truncated singular value decomposition. In this paper it will be shown that this optimal column approximation bound can be reached with only a single SVD. Moreover, it can be approximately reached in just a single approximate truncated SVD in comparison with <em>r</em> full SVDs in the original approach, thus making close to optimal column subset selection not more complex than the commonly used matrix approximation based on random projections. As a corollary, it will be shown how to find a highly nondegenerate submatrix in <em>r</em> rows of size <em>N</em> in just <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> operations, which mostly has the same properties as the maximum volume submatrix.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"725 ","pages":"Pages 359-377"},"PeriodicalIF":1.0,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670589","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 linear algebra approach to monomiality and operational methods","authors":"Luis Verde-Star","doi":"10.1016/j.laa.2025.07.019","DOIUrl":"10.1016/j.laa.2025.07.019","url":null,"abstract":"<div><div>We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are differential operators, of finite or infinite order, with polynomial coefficients. We consider the monomiality operators associated with several classes of polynomial sequences, such as Appell and Sheffer, and also orthogonal polynomial sequences that include the Meixner, Krawtchouk, Laguerre, Meixner-Pollaczek, and Hermite families.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"726 ","pages":"Pages 1-31"},"PeriodicalIF":1.0,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702565","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}