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Electronic Journal of Linear Algebra最新文献

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Sums of orthogonal, symmetric, and skew-symmetric matrices 正交、对称和斜对称矩阵的和
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-10-07 DOI: 10.13001/ela.2022.7129
Ralph John de la Cruz, Agnes T. Paras
{"title":"Sums of orthogonal, symmetric, and skew-symmetric matrices","authors":"Ralph John de la Cruz, Agnes T. Paras","doi":"10.13001/ela.2022.7129","DOIUrl":"https://doi.org/10.13001/ela.2022.7129","url":null,"abstract":"An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, and $A^T=A^{-1}$, respectively. We give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type ``\"orthogonal $+$ symmetric\" in terms of the Jordan form of $A-A^T$. We also give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type \"orthogonal $+$ skew-symmetric\" in terms of the Jordan form of $A+A^T$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45055727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Group inverses of matrices of directed trees 有向树矩阵的群逆
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-10-07 DOI: 10.13001/ela.2022.7093
R. Nandi, K. Sivakumar
{"title":"Group inverses of matrices of directed trees","authors":"R. Nandi, K. Sivakumar","doi":"10.13001/ela.2022.7093","DOIUrl":"https://doi.org/10.13001/ela.2022.7093","url":null,"abstract":"A new class of directed trees is introduced. A formula for the group inverse of the matrices associated with any tree belonging to this class is obtained. This answers affirmatively, a conjecture of Catral et al., for this new class.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48205040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
W-weighted GDMP inverse for rectangular matrices 矩形矩阵的w加权GDMP逆
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-10-06 DOI: 10.13001/ela.2022.7015
Amit Kumar, Vaibhav Shekhar, Debasisha Mishra
{"title":"W-weighted GDMP inverse for rectangular matrices","authors":"Amit Kumar, Vaibhav Shekhar, Debasisha Mishra","doi":"10.13001/ela.2022.7015","DOIUrl":"https://doi.org/10.13001/ela.2022.7015","url":null,"abstract":"In this article, we introduce two new generalized inverses for rectangular matrices called $W$-weighted generalized-Drazin--Moore--Penrose (GDMP) and $W$-weighted generalized-Drazin-reflexive (GDR) inverses. The first generalized inverse can be seen as a generalization of the recently introduced GDMP inverse for a square matrix to a rectangular matrix. The second class of generalized inverse contains the class of the first generalized inverse. We then exploit their various properties and establish that the proposed generalized inverses coincide with different well-known generalized inverses under certain assumptions. We also obtain a representation of $W$-weighted GDMP inverse employing EP-core nilpotent decomposition. We define the dual of $W$-weighted GDMP inverse and obtain analogue results. Further, we discuss additive properties, reverse- and forward-order laws for GD, $W$-weighted GD, GDMP, and $W$-weighted GDMP generalized inverses.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46166370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
A Sylvester-Kac matrix type and the Laplacian controllability of half graphs Sylvester-Kac矩阵型与半图的拉普拉斯可控性
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-09-23 DOI: 10.13001/ela.2022.6947
Milica Andelic, Carlos M. da Fonseca, E. Kılıç, Z. Stanić
{"title":"A Sylvester-Kac matrix type and the Laplacian controllability of half graphs","authors":"Milica Andelic, Carlos M. da Fonseca, E. Kılıç, Z. Stanić","doi":"10.13001/ela.2022.6947","DOIUrl":"https://doi.org/10.13001/ela.2022.6947","url":null,"abstract":"In this paper, we provide a new family of tridiagonal matrices whose eigenvalues are perfect squares. This result motivates the computation of the spectrum of a particular antibidiagonal matrix. As an application, we consider the Laplacian controllability of a particular subclass of chain graphs known as half graphs.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46298065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Unicyclic 3-colored digraphs with bicyclic inverses 具有双环逆的单环3-色有向图
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-09-15 DOI: 10.13001/ela.2022.7037
D. Kalita, K. Sarma
{"title":"Unicyclic 3-colored digraphs with bicyclic inverses","authors":"D. Kalita, K. Sarma","doi":"10.13001/ela.2022.7037","DOIUrl":"https://doi.org/10.13001/ela.2022.7037","url":null,"abstract":"The class of unicyclic $3$-colored digraphs with the cycle weight $pmmathrm{i}$ and with a unique perfect matching, denoted by $mathcal{U}_g$, is considered in this article. Kalita & Sarma [On the inverse of unicyclic 3-coloured digraphs, Linear and Multilinear Algebra, DOI: 10.1080/03081087.2021.1948956] introduced the notion of inverse of $3$-colored digraphs. They characterized the unicyclic $3$-colored digraphs in $mathcal{U}_g$ possessing unicyclic inverses. This article provides a complete characterization of the unicyclic $3$-colored digraphs in $mathcal{U}_g$ possessing bicyclic inverses.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43994716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Spectral properties of certain sequences of products of two real matrices 两个实矩阵的乘积序列的谱性质
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-08-26 DOI: 10.13001/ela.2022.6651
M. Brundu, M. Zennaro
{"title":"Spectral properties of certain sequences of products of two real matrices","authors":"M. Brundu, M. Zennaro","doi":"10.13001/ela.2022.6651","DOIUrl":"https://doi.org/10.13001/ela.2022.6651","url":null,"abstract":"\u0000\u0000\u0000The aim of this paper is to analyze the asymptotic behavior of the eigenvalues and eigenvectors of particular sequences of products involving two square real matrices $A$ and $B$, namely of the form $B^kA$, as $krightarrow infty$. This analysis represents a detailed deepening of a particular case within a general theory on finite families $mathcal{F} = { A_1, ldots, A_m }$ of real square matrices already available in the literature. The Bachmann-Landau symbols and related results are largely used and are presented in a systematic way in the final Appendix.\u0000\u0000\u0000","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":"70 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41289841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Moore-Penrose inverse of the distance matrix of a helm graph helm图距离矩阵的Moore-Penrose逆
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-08-23 DOI: 10.13001/ela.2023.7465
I. Jeyaraman, T. Divyadevi, R. Azhagendran
{"title":"The Moore-Penrose inverse of the distance matrix of a helm graph","authors":"I. Jeyaraman, T. Divyadevi, R. Azhagendran","doi":"10.13001/ela.2023.7465","DOIUrl":"https://doi.org/10.13001/ela.2023.7465","url":null,"abstract":"In this paper, we give necessary and sufficient conditions for a real symmetric matrix and, in particular, for the distance matrix $D(H_n)$ of a helm graph $H_n$ to have their Moore-Penrose inverses as the sum of a symmetric Laplacian-like matrix and a rank-one matrix. As a consequence, we present a short proof of the inverse formula, given by Goel (Linear Algebra Appl. 621:86-104, 2021), for $D(H_n)$ when $n$ is even. Further, we derive a formula for the Moore-Penrose inverse of singular $D(H_n)$ that is analogous to the formula for $D(H_n)^{-1}$. Precisely, if $n$ is odd, we find a symmetric positive semi-definite Laplacian-like matrix $L$ of order $2n-1$ and a vector $mathbf{w}in mathbb{R}^{2n-1}$ such thatbegin{eqnarray*}D(H_n)^{dagger} = -frac{1}{2}L +frac{4}{3(n-1)}mathbf{w}mathbf{w^{prime}},end{eqnarray*}where the rank of $L$ is $2n-3$. We also investigate the inertia of $D(H_n)$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44270804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
The products of involutions in a matrix centralizer 矩阵扶正器中对合的乘积
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-08-20 DOI: 10.13001/ela.2022.7091
Ralph John de la Cruz, Raymond Louis Tañedo
{"title":"The products of involutions in a matrix centralizer","authors":"Ralph John de la Cruz, Raymond Louis Tañedo","doi":"10.13001/ela.2022.7091","DOIUrl":"https://doi.org/10.13001/ela.2022.7091","url":null,"abstract":"A square matrix $A$ is an involution if $A^{2} = I$. The centralizer of a square matrix $S$ denoted by $mathscr{C}(S)$ is the set of all $A$ such that $AS = SA$ over an algebraically closed field of characteristic not equal to 2. We determine necessary and sufficient conditions for $A in mathscr{C}(S)$ to be a product of involutions in $mathscr{C}(S)$ where $S$ is a basic Weyr matrix with homogeneous Weyr structure of length 3. Finally, we will show some results for the case when the length of the Weyr structure is greater than 3.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41919464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
On m-th roots of complex matrices 在复矩阵的m次根上
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-08-20 DOI: 10.13001/ela.2022.7047
H. Liu, Jing Zhao
{"title":"On m-th roots of complex matrices","authors":"H. Liu, Jing Zhao","doi":"10.13001/ela.2022.7047","DOIUrl":"https://doi.org/10.13001/ela.2022.7047","url":null,"abstract":"For an $ntimes n$ matrix $M$, $sigma(M)$ denotes the set of all different eigenvalues of $M$. In this paper, we will prove two results on the $m$-th $(mgeq2)$ roots of a matrix $A$. Firstly, let $X$ be an $m$-th root of $A$. Then $X$ can be expressed as a polynomial in $A$ if and only if rank $X^2$= rank $X$ and $|sigma(X)|=|sigma(A)|$. Secondly, let $X$ and $Y$ be two $m$-th roots of $A$. If both $X$ and $Y$ can be expressed as polynomials in $A$, then $X=Y$ if and only if $sigma(X)=sigma(Y)$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44485991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A note on bounds for eigenvalues of nonsingular H-tensors 关于非奇异h张量特征值界的一个注记
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2022-08-20 DOI: 10.13001/ela.2022.7097
Jun He, Guanjun Xu
{"title":"A note on bounds for eigenvalues of nonsingular H-tensors","authors":"Jun He, Guanjun Xu","doi":"10.13001/ela.2022.7097","DOIUrl":"https://doi.org/10.13001/ela.2022.7097","url":null,"abstract":"A counterexample to a theorem in the paper ELA 29:3-16, (2015) is provided, and an upper bound on the H-spectral radius of H-tensors is given.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44861301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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