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Isometries of the qubit state space with respect to quantum Wasserstein distances
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-03-13 DOI: 10.1016/j.laa.2025.03.004
Richárd Simon , Dániel Virosztek
{"title":"Isometries of the qubit state space with respect to quantum Wasserstein distances","authors":"Richárd Simon ,&nbsp;Dániel Virosztek","doi":"10.1016/j.laa.2025.03.004","DOIUrl":"10.1016/j.laa.2025.03.004","url":null,"abstract":"<div><div>In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence <span><math><msub><mrow><mi>d</mi></mrow><mrow><mtext>sym</mtext></mrow></msub></math></span>, the divergence induced by all of the Pauli matrices. We also give a complete characterization of isometries with respect to <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>, the quantum Wasserstein distance corresponding to the single Pauli matrix <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"714 ","pages":"Pages 1-14"},"PeriodicalIF":1.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structured backward errors for special classes of saddle point problems with applications
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-03-10 DOI: 10.1016/j.laa.2025.03.003
Sk. Safique Ahmad, Pinki Khatun
{"title":"Structured backward errors for special classes of saddle point problems with applications","authors":"Sk. Safique Ahmad,&nbsp;Pinki Khatun","doi":"10.1016/j.laa.2025.03.003","DOIUrl":"10.1016/j.laa.2025.03.003","url":null,"abstract":"<div><div>In the realm of numerical analysis, the study of structured backward errors (<em>BEs</em>) in saddle point problems (<em>SPPs</em>) has shown promising potential for development. However, these investigations overlook the inherent sparsity pattern of the coefficient matrix of the <em>SPP</em>. Moreover, the existing techniques are not applicable when the block matrices have <em>circulant</em>, <em>Toeplitz</em>, or <em>symmetric</em>-<em>Toeplitz</em> structures and do not even provide structure-preserving minimal perturbation matrices for which the <em>BE</em> is attained. To overcome these limitations, we investigate the structured <em>BEs</em> of <em>SPPs</em> when the perturbation matrices exploit the sparsity pattern as well as <em>circulant</em>, <em>Toeplitz</em>, and <em>symmetric</em>-<em>Toeplitz</em> structures. Furthermore, we construct minimal perturbation matrices that preserve the sparsity pattern and the aforementioned structures. Applications of the developed frameworks are utilized to compute <em>BEs</em> for the weighted regularized least squares problem. Finally, numerical experiments are performed to validate our findings, showcasing the utility of the obtained structured <em>BEs</em> in assessing the strong backward stability of numerical algorithms.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"713 ","pages":"Pages 90-112"},"PeriodicalIF":1.0,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143631968","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}
引用次数: 0
The full P-vertex problem for unicyclic graphs
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-03-06 DOI: 10.1016/j.laa.2025.02.024
A. Howlader, P.R. Raickwade, K.C. Sivakumar
{"title":"The full P-vertex problem for unicyclic graphs","authors":"A. Howlader,&nbsp;P.R. Raickwade,&nbsp;K.C. Sivakumar","doi":"10.1016/j.laa.2025.02.024","DOIUrl":"10.1016/j.laa.2025.02.024","url":null,"abstract":"<div><div>Let <em>A</em> be a real symmetric and nonsingular matrix and <em>G</em> be the underlying graph. Let <span><math><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo></math></span> be the principal submatrix obtained by removing the <span><math><msup><mrow><mi>i</mi></mrow><mrow><mtext>th</mtext></mrow></msup></math></span> row and the <span><math><msup><mrow><mi>i</mi></mrow><mrow><mtext>th</mtext></mrow></msup></math></span> column of <em>A</em>. If the nullity of <span><math><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo></math></span> is unity, then the vertex <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is called a P-vertex of the matrix <em>A</em>. The full P-vertex problem is to determine if there is a nonsingular matrix <em>A</em> such that each vertex of the corresponding graph <em>G</em>, is a P-vertex of <em>A</em>. In this article, we investigate the full P-vertex problem for unicyclic graphs.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"713 ","pages":"Pages 74-89"},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143631967","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}
引用次数: 0
Interplay between discretization and controllability of linear delay systems: An algebraic viewpoint
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-03-03 DOI: 10.1016/j.laa.2025.02.025
Florentina Nicolau , Hugues Mounier , Silviu-Iulian Niculescu
{"title":"Interplay between discretization and controllability of linear delay systems: An algebraic viewpoint","authors":"Florentina Nicolau ,&nbsp;Hugues Mounier ,&nbsp;Silviu-Iulian Niculescu","doi":"10.1016/j.laa.2025.02.025","DOIUrl":"10.1016/j.laa.2025.02.025","url":null,"abstract":"<div><div>In this paper, we give an in depth study of linear delay systems controllability preservation/alteration through discretization. We make use of a module theoretic framework acting as a unifying one for most of the existing delay system controllability notions. We propose a formal generic definition of a discretization scheme and illustrate through examples that controllability properties may be lost through discretization. Then, we introduce the notion of preservation (that is, a measure of quantifying the ability of the discretizer to preserve controllability properties) and prove that for a given discretizer, we can always find a delay system for which even the torsion-free controllability (which is the weakest controllability notion) is not preserved. Finally, we reverse the situation, and show that for any given delay system, preserving discretizers exist.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"713 ","pages":"Pages 18-73"},"PeriodicalIF":1.0,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621477","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}
引用次数: 0
Two-generation of traceless matrices over finite fields
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-02-28 DOI: 10.1016/j.laa.2025.02.023
Omer Cantor , Urban Jezernik , Andoni Zozaya
{"title":"Two-generation of traceless matrices over finite fields","authors":"Omer Cantor ,&nbsp;Urban Jezernik ,&nbsp;Andoni Zozaya","doi":"10.1016/j.laa.2025.02.023","DOIUrl":"10.1016/j.laa.2025.02.023","url":null,"abstract":"<div><div>We prove that the Lie algebra <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math></span> of traceless matrices over a finite field of characteristic <em>p</em> can be generated by 2 elements with exceptions when <span><math><mo>(</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></span> is <span><math><mo>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span> or <span><math><mo>(</mo><mn>4</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>. In the latter cases, we establish curious identities that obstruct 2-generation.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"713 ","pages":"Pages 1-17"},"PeriodicalIF":1.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143547843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved error bounds for the deflated multi-preconditioned CG method
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-02-25 DOI: 10.1016/j.laa.2025.02.022
Reinhard Nabben, Julian Schramm
{"title":"Improved error bounds for the deflated multi-preconditioned CG method","authors":"Reinhard Nabben,&nbsp;Julian Schramm","doi":"10.1016/j.laa.2025.02.022","DOIUrl":"10.1016/j.laa.2025.02.022","url":null,"abstract":"<div><div>Preconditioning and deflation are well-known techniques to speed up the convergence of the CG method. The concept of multiple-preconditioning however is introduced in the last decade. Recently, in <span><span>[21]</span></span>, a new adaptive preconditioned CG method is established that combines all these techniques. The main tool of the adaptive method is a new error bound for the deflated preconditioned CG method. Using this bound it is decided in each iteration if the deflated preconditioned CG method is sufficient in reducing the error or whether an acceleration by performing iterations of the multi-preconditioned CG method is needed. Here we improve this error bound. This new bound contributes to the theory of deflation methods but can also lead to new decision rules for the adaptive multi-preconditioned CG method.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"712 ","pages":"Pages 29-48"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
State transfer and readout times for trees of diameter 4
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-02-19 DOI: 10.1016/j.laa.2025.02.021
Stephen Kirkland , Christopher M. van Bommel
{"title":"State transfer and readout times for trees of diameter 4","authors":"Stephen Kirkland ,&nbsp;Christopher M. van Bommel","doi":"10.1016/j.laa.2025.02.021","DOIUrl":"10.1016/j.laa.2025.02.021","url":null,"abstract":"<div><div>We consider the state transfer properties of continuous time quantum walks on trees of diameter 4. We characterize all pairs of strongly cospectral vertices in trees of diameter 4, finding that they fall into pairs of three different types. For each type, we construct an infinite family of diameter 4 trees for which there is pretty good state transfer between the pair of strongly cospectral vertices. Moreover, for two of those types, for each tree in the infinite family, we give an explicit sequence of readout times at which the fidelity of state transfer converges to 1. For strongly cospectral vertices of the remaining type, we identify a sequence of trees and explicit readout times so that the fidelity of state transfer between the strongly cospectral vertices approaches 1.</div><div>We also prove a result of independent interest: for a graph with the property that the fidelity of state transfer between a pair of vertices at time <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> converges to 1 as <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span>, then the derivative of the fidelity at <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> converges to 0 as <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"712 ","pages":"Pages 9-28"},"PeriodicalIF":1.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511965","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}
引用次数: 0
Number of characteristic polynomials of matrices with bounded height
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-02-19 DOI: 10.1016/j.laa.2025.02.012
László Mérai , Igor E. Shparlinski
{"title":"Number of characteristic polynomials of matrices with bounded height","authors":"László Mérai ,&nbsp;Igor E. Shparlinski","doi":"10.1016/j.laa.2025.02.012","DOIUrl":"10.1016/j.laa.2025.02.012","url":null,"abstract":"<div><div>We consider the set <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>Z</mi><mo>;</mo><mi>H</mi><mo>)</mo></mrow></math></span> of <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span>-matrices with integer elements of size at most <em>H</em> and obtain upper and lower bounds on the number of distinct irreducible characteristic polynomials which correspond to these matrices and thus on the number of distinct eigenvalues of these matrices. In particular, we improve some results of A. Abrams, Z. Landau, J. Pommersheim and N. Srivastava (2022).</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"712 ","pages":"Pages 1-8"},"PeriodicalIF":1.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508739","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}
引用次数: 0
On Picard groups and Jacobians of directed graphs
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-02-18 DOI: 10.1016/j.laa.2025.02.020
Jaiung Jun , Youngsu Kim , Matthew Pisano
{"title":"On Picard groups and Jacobians of directed graphs","authors":"Jaiung Jun ,&nbsp;Youngsu Kim ,&nbsp;Matthew Pisano","doi":"10.1016/j.laa.2025.02.020","DOIUrl":"10.1016/j.laa.2025.02.020","url":null,"abstract":"<div><div>The Picard group of an undirected graph is a finitely generated abelian group, and the Jacobian is the torsion subgroup of the Picard group. These groups can be computed by using the Smith normal form of the Laplacian matrix of the graph or by using chip-firing games associated with the graph. One may consider its generalization to directed graphs based on the Laplacian matrix. We compute Picard groups and Jacobians for several classes of directed trees, cycles, wheel, and multipartite graphs.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"711 ","pages":"Pages 180-211"},"PeriodicalIF":1.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474627","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}
引用次数: 0
Invariant subspace perturbation of a matrix with Jordan blocks
IF 1 3区 数学
Linear Algebra and its Applications Pub Date : 2025-02-14 DOI: 10.1016/j.laa.2025.02.019
Hongguo Xu
{"title":"Invariant subspace perturbation of a matrix with Jordan blocks","authors":"Hongguo Xu","doi":"10.1016/j.laa.2025.02.019","DOIUrl":"10.1016/j.laa.2025.02.019","url":null,"abstract":"<div><div>We investigate how invariant subspaces corresponding to a single eigenvalue will change when a matrix is perturbed. We focus on the invariant subspaces corresponding to an eigenvalue associated with the Jordan blocks that have the same size. An invariant subspace can be expressed as the range of a full column matrix. We characterize the perturbed invariant subspaces with such matrices expressed in a sum form that exhibits the fractional orders. We also provide the formulas for the coefficient matrices associated with the zero and first fractional orders. The results extend the standard invariant subspace perturbation theory.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"711 ","pages":"Pages 143-179"},"PeriodicalIF":1.0,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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