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The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices 具有n个顶点的双环图和三环图补集的Aα谱半径
IF 0.5
Special Matrices Pub Date : 2021-09-25 DOI: 10.1515/spma-2021-0147
Chaohui Chen, Jiarong Peng, Tianyuan Chen
{"title":"The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices","authors":"Chaohui Chen, Jiarong Peng, Tianyuan Chen","doi":"10.1515/spma-2021-0147","DOIUrl":"https://doi.org/10.1515/spma-2021-0147","url":null,"abstract":"Abstract Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely. In this paper, we extend the largest ordering of Aα -spectral radius among all complements of bicyclic and tricyclic graphs with n vertices, respectively.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"56 - 66"},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45241113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Singular matrices that are products of two idempotents or products of two nilpotents 奇异矩阵是两个幂等矩阵或两个幂零矩阵的乘积
IF 0.5
Special Matrices Pub Date : 2021-09-17 DOI: 10.1515/spma-2021-0146
G. Călugăreanu
{"title":"Singular matrices that are products of two idempotents or products of two nilpotents","authors":"G. Călugăreanu","doi":"10.1515/spma-2021-0146","DOIUrl":"https://doi.org/10.1515/spma-2021-0146","url":null,"abstract":"Abstract Over commutative domains we characterize the singular 2 × 2 matrices which are products of two idempotents or products of two nilpotents. The relevant casees are the matrices with zero second row and the singular matrices with only nonzero entries.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"47 - 55"},"PeriodicalIF":0.5,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45657897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Steiner distance matrix of caterpillar graphs 毛虫图的Steiner距离矩阵
IF 0.5
Special Matrices Pub Date : 2021-08-29 DOI: 10.1515/spma-2022-0162
A. Azimi, R. Bapat, S. Goel
{"title":"Steiner distance matrix of caterpillar graphs","authors":"A. Azimi, R. Bapat, S. Goel","doi":"10.1515/spma-2022-0162","DOIUrl":"https://doi.org/10.1515/spma-2022-0162","url":null,"abstract":"Abstract In this article, we show that the rank of the 2-Steiner distance matrix of a caterpillar graph having NN vertices and pp pendant veritices is 2N−p−12N-p-1.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"267 - 284"},"PeriodicalIF":0.5,"publicationDate":"2021-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45543374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix Fibonacci-Sylvester-Kac矩阵的特征多项式、行列式和逆
IF 0.5
Special Matrices Pub Date : 2021-08-23 DOI: 10.1515/spma-2021-0145
Zhaolin Jiang, Yanpeng Zheng, Tianzi Li
{"title":"Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix","authors":"Zhaolin Jiang, Yanpeng Zheng, Tianzi Li","doi":"10.1515/spma-2021-0145","DOIUrl":"https://doi.org/10.1515/spma-2021-0145","url":null,"abstract":"Abstract In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"40 - 46"},"PeriodicalIF":0.5,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45577629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On eigenvalues of a matrix arising in energy-preserving/dissipative continuous-stage Runge-Kutta methods 关于保能/耗散连续阶段Runge-Kutta方法中矩阵的特征值
IF 0.5
Special Matrices Pub Date : 2021-08-10 DOI: 10.1515/spma-2021-0101
Yusaku Yamamoto
{"title":"On eigenvalues of a matrix arising in energy-preserving/dissipative continuous-stage Runge-Kutta methods","authors":"Yusaku Yamamoto","doi":"10.1515/spma-2021-0101","DOIUrl":"https://doi.org/10.1515/spma-2021-0101","url":null,"abstract":"Abstract In this short note, we define an s × s matrix Ks constructed from the Hilbert matrix Hs=(1i+j-1)i,j=1s{H_s} = left( {{1 over {i + j - 1}}} right)_{i,j = 1}^s and prove that it has at least one pair of complex eigenvalues when s ≥ 2. Ks is a matrix related to the AVF collocation method, which is an energy-preserving/dissipative numerical method for ordinary differential equations, and our result gives a matrix-theoretical proof that the method does not have large-grain parallelism when its order is larger than or equal to 4.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"34 - 39"},"PeriodicalIF":0.5,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43973466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Eccentricity energy change of complete multipartite graphs due to edge deletion 完全多部分图由于边缘删除引起的偏心能量变化
IF 0.5
Special Matrices Pub Date : 2021-07-07 DOI: 10.1515/spma-2021-0156
Iswar Mahato, M. Kannan
{"title":"Eccentricity energy change of complete multipartite graphs due to edge deletion","authors":"Iswar Mahato, M. Kannan","doi":"10.1515/spma-2021-0156","DOIUrl":"https://doi.org/10.1515/spma-2021-0156","url":null,"abstract":"Abstract The eccentricity matrix ɛ(G) of a graph G is obtained from the distance matrix of G by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of G is sum of the absolute values of the eigenvalues of ɛ(G). Although the eccentricity matrices of graphs are closely related to the distance matrices of graphs, a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The change in eccentricity energy of a graph due to an edge deletion is one such property. In this article, we give examples of graphs for which the eccentricity energy increase (resp., decrease) but the distance energy decrease (resp., increase) due to an edge deletion. Also, we prove that the eccentricity energy of the complete k-partite graph Kn1,...,nk with k ≥ 2 and ni ≥ 2, increases due to an edge deletion.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"193 - 202"},"PeriodicalIF":0.5,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49574284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Perturbation analysis for the Takagi vector matrix Takagi向量矩阵的扰动分析
IF 0.5
Special Matrices Pub Date : 2021-07-03 DOI: 10.1515/spma-2020-0144
A. Farooq, M. Samar, Rewayat Khan, Hanyu Li, M. Kamran
{"title":"Perturbation analysis for the Takagi vector matrix","authors":"A. Farooq, M. Samar, Rewayat Khan, Hanyu Li, M. Kamran","doi":"10.1515/spma-2020-0144","DOIUrl":"https://doi.org/10.1515/spma-2020-0144","url":null,"abstract":"Abstract In this article, we present some perturbation bounds for the Takagi vector matrix when the original matrix undergoes the additive or multiplicative perturbation. Two numerical examples are given to illuminate these bounds.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"23 - 33"},"PeriodicalIF":0.5,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/spma-2020-0144","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44986505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields 有限域上增强主秩特征序列的组合性质
IF 0.5
Special Matrices Pub Date : 2021-06-12 DOI: 10.1515/spma-2021-0154
P. Dukes, Xavier Mart'inez-Rivera
{"title":"Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields","authors":"P. Dukes, Xavier Mart'inez-Rivera","doi":"10.1515/spma-2021-0154","DOIUrl":"https://doi.org/10.1515/spma-2021-0154","url":null,"abstract":"Abstract The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽n×n is defined as ℓ1ℓ2· · · ℓn, where ℓj ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero. Building upon the second author’s recent classification of the epr-sequences of symmetric matrices over the field 𝔽 = 𝔽2, we initiate a study of the case 𝔽= 𝔽3. Moreover, epr-sequences over finite fields are shown to have connections to Ramsey theory and coding theory.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"166 - 179"},"PeriodicalIF":0.5,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49544831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse properties of a class of seven-diagonal (near) Toeplitz matrices 一类七对角(近)Toeplitz矩阵的逆性质
IF 0.5
Special Matrices Pub Date : 2021-03-17 DOI: 10.1515/spma-2021-0148
B. Kurmanbek, Y. Erlangga, Y. Amanbek
{"title":"Inverse properties of a class of seven-diagonal (near) Toeplitz matrices","authors":"B. Kurmanbek, Y. Erlangga, Y. Amanbek","doi":"10.1515/spma-2021-0148","DOIUrl":"https://doi.org/10.1515/spma-2021-0148","url":null,"abstract":"Abstract This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"67 - 86"},"PeriodicalIF":0.5,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42891529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the similarity to nonnegative and Metzler Hessenberg forms 关于非负形式和Metzler-Hessenberg形式的相似性
IF 0.5
Special Matrices Pub Date : 2021-03-08 DOI: 10.1515/spma-2020-0140
Christian Grussler, A. Rantzer
{"title":"On the similarity to nonnegative and Metzler Hessenberg forms","authors":"Christian Grussler, A. Rantzer","doi":"10.1515/spma-2020-0140","DOIUrl":"https://doi.org/10.1515/spma-2020-0140","url":null,"abstract":"Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"1 - 8"},"PeriodicalIF":0.5,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/spma-2020-0140","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49552411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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