Pub Date : 2025-10-10DOI: 10.1016/j.laa.2025.10.009
Emil Graf, Alex Townsend
We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are constructed at intermediate steps. In particular, we give multidimensional polynomial systems for which the conditioning of a subproblem can be worse than the conditioning of the original problem by a factor that grows exponentially with the number of variables.
{"title":"Numerical instability of algebraic rootfinders","authors":"Emil Graf, Alex Townsend","doi":"10.1016/j.laa.2025.10.009","DOIUrl":"10.1016/j.laa.2025.10.009","url":null,"abstract":"<div><div>We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are constructed at intermediate steps. In particular, we give multidimensional polynomial systems for which the conditioning of a subproblem can be worse than the conditioning of the original problem by a factor that grows exponentially with the number of variables.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 308-336"},"PeriodicalIF":1.1,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145322124","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}
Pub Date : 2025-10-10DOI: 10.1016/j.laa.2025.10.007
Hwa-Long Gau , Pei Yuan Wu
For a bounded linear operator A on a complex Hilbert space H, we consider the implication relationships of the following properties: (1) A is a ρ-contraction for some , (2) exists for all x in H, (3) A is similar to a contraction, (4) A is polynomially bounded, (5) A is power-bounded, and (6) the spectral radius of A is at most 1. Some of the implications were known to be false before. We show that any noncontractive idempotent operator A satisfies (2) and (3) but not (1), and if A acts on a finite-dimensional H, then (2) implies (3) and (3), (4), and (5) are equivalent. Moreover, (5) easily implies (6) and the converse is false.
{"title":"ρ-Contraction and its consequences","authors":"Hwa-Long Gau , Pei Yuan Wu","doi":"10.1016/j.laa.2025.10.007","DOIUrl":"10.1016/j.laa.2025.10.007","url":null,"abstract":"<div><div>For a bounded linear operator <em>A</em> on a complex Hilbert space <em>H</em>, we consider the implication relationships of the following properties: (1) <em>A</em> is a <em>ρ</em>-contraction for some <span><math><mi>ρ</mi><mo>></mo><mn>0</mn></math></span>, (2) <span><math><msub><mrow><mi>lim</mi></mrow><mrow><mi>n</mi></mrow></msub><mo></mo><mo>‖</mo><msup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>x</mi><mo>‖</mo></math></span> exists for all <em>x</em> in <em>H</em>, (3) <em>A</em> is similar to a contraction, (4) <em>A</em> is polynomially bounded, (5) <em>A</em> is power-bounded, and (6) the spectral radius of <em>A</em> is at most 1. Some of the implications were known to be false before. We show that any noncontractive idempotent operator <em>A</em> satisfies (2) and (3) but not (1), and if <em>A</em> acts on a finite-dimensional <em>H</em>, then (2) implies (3) and (3), (4), and (5) are equivalent. Moreover, (5) easily implies (6) and the converse is false.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 246-255"},"PeriodicalIF":1.1,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145322087","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}
Pub Date : 2025-10-10DOI: 10.1016/j.laa.2025.10.006
Y. Kulev, A. Maksaev, V.V. Promyslov
The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This concept can be reformulated in terms of Boolean matrices and extended to all matrices, not only primitive. In this paper, for , we completely characterize additive maps that preserve two different values of λ-th upper scrambling index belonging to , or strongly preserve one fixed value.
{"title":"Maps preserving two small values of λ-th upper scrambling index","authors":"Y. Kulev, A. Maksaev, V.V. Promyslov","doi":"10.1016/j.laa.2025.10.006","DOIUrl":"10.1016/j.laa.2025.10.006","url":null,"abstract":"<div><div>The notion of <em>λ</em>-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph <em>D</em>, it is defined as the smallest positive integer <em>k</em> such that for every <em>λ</em> vertices of <em>D</em> there exist directed paths of lengths <em>k</em> from these vertices to a common vertex. This concept can be reformulated in terms of Boolean matrices and extended to all <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices, not only primitive. In this paper, for <span><math><mi>λ</mi><mo>></mo><mn>1</mn></math></span>, we completely characterize additive maps that preserve two different values of <em>λ</em>-th upper scrambling index belonging to <span><math><mo>[</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span>, or strongly preserve one fixed value.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"730 ","pages":"Pages 51-72"},"PeriodicalIF":1.1,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145323237","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}
Pub Date : 2025-10-10DOI: 10.1016/j.laa.2025.10.003
Simon Mataigne , P.-A. Absil , Nina Miolane
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by Hüper et al. (2021), which contains the well-known Euclidean and canonical metrics. First, we give the best Lipschitz constants between the distances induced by any two members of the family of metrics. Then, we give a lower and an upper bound on the geodesic distance by the easily computable Frobenius distance. We give explicit families of pairs of matrices that depend on the parameter of the metric and the dimensions of the manifold, where the lower and the upper bound are attained. These bounds aim at improving the theoretical guarantees and performance of minimal geodesic computation algorithms by reducing the initial velocity search space. In addition, these findings contribute to advancing the understanding of geodesic distances on the Stiefel manifold and their applications.
{"title":"Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics","authors":"Simon Mataigne , P.-A. Absil , Nina Miolane","doi":"10.1016/j.laa.2025.10.003","DOIUrl":"10.1016/j.laa.2025.10.003","url":null,"abstract":"<div><div>We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by Hüper et al. (2021), which contains the well-known Euclidean and canonical metrics. First, we give the best Lipschitz constants between the distances induced by any two members of the family of metrics. Then, we give a lower and an upper bound on the geodesic distance by the easily computable Frobenius distance. We give explicit families of pairs of matrices that depend on the parameter of the metric and the dimensions of the manifold, where the lower and the upper bound are attained. These bounds aim at improving the theoretical guarantees and performance of minimal geodesic computation algorithms by reducing the initial velocity search space. In addition, these findings contribute to advancing the understanding of geodesic distances on the Stiefel manifold and their applications.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"730 ","pages":"Pages 1-34"},"PeriodicalIF":1.1,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145323235","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}
Pub Date : 2025-10-10DOI: 10.1016/j.laa.2025.10.008
Nguyen Thi Thai Ha , Ngo Le Hong Phuc , Vu Mai Trang
Let be the special linear group over a division algebra D with . A matrix is called a k-involution if and . We show that every matrix can be written as a product of at most 2-involutions, where , and denotes the commutator width of D. The result remains valid when expressing matrices as products of k-involutions for arbitrary , and we establish explicit upper bounds for their corresponding k-involution lengths.
{"title":"Lengths of matrix decompositions over division algebras with k-involutions","authors":"Nguyen Thi Thai Ha , Ngo Le Hong Phuc , Vu Mai Trang","doi":"10.1016/j.laa.2025.10.008","DOIUrl":"10.1016/j.laa.2025.10.008","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span> be the special linear group over a division algebra <em>D</em> with <span><math><mi>char</mi><mo>(</mo><mi>D</mi><mo>)</mo><mo>≠</mo><mn>2</mn></math></span>. A matrix <span><math><mi>A</mi><mo>∈</mo><msub><mrow><mi>SL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span> is called a <em>k</em>-involution if <span><math><mi>rank</mi><mo>(</mo><mi>A</mi><mo>−</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>=</mo><mi>k</mi></math></span> and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We show that every matrix <span><math><mi>A</mi><mo>∈</mo><msub><mrow><mi>SL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span> can be written as a product of at most <span><math><mrow><mo>⌈</mo><mfrac><mrow><mi>res</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></mrow><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mi>ω</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> 2-involutions, where <span><math><mi>res</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>rank</mi><mo>(</mo><mi>A</mi><mo>−</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>, and <span><math><mi>ω</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> denotes the commutator width of <em>D</em>. The result remains valid when expressing matrices as products of <em>k</em>-involutions for arbitrary <span><math><mi>k</mi><mo>></mo><mn>1</mn></math></span>, and we establish explicit upper bounds for their corresponding k-involution lengths.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 337-349"},"PeriodicalIF":1.1,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363878","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}
Pub Date : 2025-10-10DOI: 10.1016/j.laa.2025.10.005
Yongang Wang , Francesco Belardo , Dan Li
The eigenvalues of a signed graph are the eigenvalues of its adjacency matrix. In this paper, we consider the problem of identifying the signed graphs with a small number of positive eigenvalues. We characterize the complete signed graphs having exactly two positive eigenvalues. In addition, we completely characterize the complete bipartite signed graphs having exactly three positive eigenvalues.
{"title":"On signed graphs with at most three positive eigenvalues","authors":"Yongang Wang , Francesco Belardo , Dan Li","doi":"10.1016/j.laa.2025.10.005","DOIUrl":"10.1016/j.laa.2025.10.005","url":null,"abstract":"<div><div>The eigenvalues of a signed graph are the eigenvalues of its adjacency matrix. In this paper, we consider the problem of identifying the signed graphs with a small number of positive eigenvalues. We characterize the complete signed graphs having exactly two positive eigenvalues. In addition, we completely characterize the complete bipartite signed graphs having exactly three positive eigenvalues.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 293-307"},"PeriodicalIF":1.1,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145322123","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}
Pub Date : 2025-10-09DOI: 10.1016/j.laa.2025.10.002
Peter Danchev , Esther García , Miguel Gómez Lozano
Let be a finite field of odd characteristic. When , we prove that every matrix A admits a decomposition into , where D is diagonalizable and . For , we show that such a decomposition is possible for non-derogatory matrices of order at least 5, and more generally, for matrices whose first invariant factor is not a non-zero trace irreducible polynomial of degree 3; we also establish that matrices consisting of direct sums of companion matrices, all of them associated to the same irreducible polynomial of non-zero trace and degree 3 over , never admit such a decomposition.
These results completely settle the question posed by Breaz (2018) [3] asking if it is true that, for big enough positive integers , all matrices A over a field of odd cardinality q admit decompositions of the form with and : specifically, the answer is yes for , but however there are counterexamples for and each order , whenever .
{"title":"Matrices over finite fields of odd characteristic as sums of diagonalizable and square-zero matrices","authors":"Peter Danchev , Esther García , Miguel Gómez Lozano","doi":"10.1016/j.laa.2025.10.002","DOIUrl":"10.1016/j.laa.2025.10.002","url":null,"abstract":"<div><div>Let <span><math><mi>F</mi></math></span> be a finite field of odd characteristic. When <span><math><mo>|</mo><mi>F</mi><mo>|</mo><mo>≥</mo><mn>5</mn></math></span>, we prove that every matrix <em>A</em> admits a decomposition into <span><math><mi>D</mi><mo>+</mo><mi>M</mi></math></span>, where <em>D</em> is diagonalizable and <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></math></span>. For <span><math><mi>F</mi><mo>=</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, we show that such a decomposition is possible for non-derogatory matrices of order at least 5, and more generally, for matrices whose first invariant factor is not a non-zero trace irreducible polynomial of degree 3; we also establish that matrices consisting of direct sums of companion matrices, all of them associated to the same irreducible polynomial of non-zero trace and degree 3 over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, never admit such a decomposition.</div><div>These results completely settle the question posed by Breaz (2018) <span><span>[3]</span></span> asking if it is true that, for big enough positive integers <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, all matrices <em>A</em> over a field of odd cardinality <em>q</em> admit decompositions of the form <span><math><mi>E</mi><mo>+</mo><mi>M</mi></math></span> with <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>=</mo><mi>E</mi></math></span> and <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></math></span>: specifically, the answer is <em>yes</em> for <span><math><mi>q</mi><mo>≥</mo><mn>5</mn></math></span>, but however there are counterexamples for <span><math><mi>q</mi><mo>=</mo><mn>3</mn></math></span> and each order <span><math><mi>n</mi><mo>=</mo><mn>3</mn><mi>k</mi></math></span>, whenever <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"730 ","pages":"Pages 35-50"},"PeriodicalIF":1.1,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145323236","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}
Pub Date : 2025-10-07DOI: 10.1016/j.laa.2025.09.025
Hongxin Chen , Caixing Gu , Shuaibing Luo , Shan Wang
In this paper, we show that any infinite isometric commuting tuple on a finite dimensional Hilbert space is a finite isometry. We then completely characterize the m-isometric commuting tuple on a finite dimensional Hilbert space for any positive integer m.
{"title":"Higher order isometric commuting tuples on finite dimensional Hilbert spaces","authors":"Hongxin Chen , Caixing Gu , Shuaibing Luo , Shan Wang","doi":"10.1016/j.laa.2025.09.025","DOIUrl":"10.1016/j.laa.2025.09.025","url":null,"abstract":"<div><div>In this paper, we show that any infinite isometric commuting tuple on a finite dimensional Hilbert space is a finite isometry. We then completely characterize the <em>m</em>-isometric commuting tuple on a finite dimensional Hilbert space for any positive integer <em>m</em>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 223-245"},"PeriodicalIF":1.1,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269880","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}
Pub Date : 2025-10-03DOI: 10.1016/j.laa.2025.09.021
Ping-Fan Dai , Yan-Ping Liu
Accurate inverses of structured matrices are desired for application areas of numerical linear algebra. matrices are introduced in Peña (2011) [6]. In this paper, a parametrization of an Z-matrix is investigated. Then the inverses of Z-matrices are computed to high relative accuracy under a weak assumption. Numerical examples are used to illustrate the accuracy of the inverse for the matrices.
{"title":"Accurate inverses for SDD1 Z-matrices","authors":"Ping-Fan Dai , Yan-Ping Liu","doi":"10.1016/j.laa.2025.09.021","DOIUrl":"10.1016/j.laa.2025.09.021","url":null,"abstract":"<div><div>Accurate inverses of structured matrices are desired for application areas of numerical linear algebra. <span><math><mi>S</mi><mi>D</mi><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> matrices are introduced in Peña (2011) <span><span>[6]</span></span>. In this paper, a parametrization of an <span><math><mi>S</mi><mi>D</mi><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> <em>Z</em>-matrix is investigated. Then the inverses of <span><math><mi>S</mi><mi>D</mi><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> <em>Z</em>-matrices are computed to high relative accuracy under a weak assumption. Numerical examples are used to illustrate the accuracy of the inverse for the matrices.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 203-222"},"PeriodicalIF":1.1,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269879","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}
Pub Date : 2025-10-02DOI: 10.1016/j.laa.2025.09.026
Yu-Chen Fu , Gui-Xian Tian , Shu-Yu Cui , Fen-Fang Ren
In the field of spectral graph theory, the problem of constructing cospectral graphs has long been an important topic of discussion among researchers. There are mainly two methods for constructing cospectral graphs. One is to construct pairs of cospectral graphs by performing operations or switches on the edge sets of graphs, and the other is to utilize some operations between graphs to generate a large number of pairs of cospectral graphs. This paper proposes a novel method for constructing graphs. Moreover, in some special cases, the spectra of the graphs constructed by this method are characterized using the corresponding spectra of the factor graphs. Finally, with the help of the above results, several consequences regarding the construction of cospectral graphs are presented.
{"title":"Constructing cospectral graphs via exotic graph products","authors":"Yu-Chen Fu , Gui-Xian Tian , Shu-Yu Cui , Fen-Fang Ren","doi":"10.1016/j.laa.2025.09.026","DOIUrl":"10.1016/j.laa.2025.09.026","url":null,"abstract":"<div><div>In the field of spectral graph theory, the problem of constructing cospectral graphs has long been an important topic of discussion among researchers. There are mainly two methods for constructing cospectral graphs. One is to construct pairs of cospectral graphs by performing operations or switches on the edge sets of graphs, and the other is to utilize some operations between graphs to generate a large number of pairs of cospectral graphs. This paper proposes a novel method for constructing graphs. Moreover, in some special cases, the spectra of the graphs constructed by this method are characterized using the corresponding spectra of the factor graphs. Finally, with the help of the above results, several consequences regarding the construction of cospectral graphs are presented.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 148-166"},"PeriodicalIF":1.1,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269883","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}
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