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Electronic Journal of Linear Algebra最新文献

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The matrix inverse Young inequality 矩阵逆Young不等式
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-04-07 DOI: 10.13001/ela.2023.7773
S. Drury
{"title":"The matrix inverse Young inequality","authors":"S. Drury","doi":"10.13001/ela.2023.7773","DOIUrl":"https://doi.org/10.13001/ela.2023.7773","url":null,"abstract":"An inverse Young inequality is established for positive definite matrices.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49306847","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
Fields of U-invariants of matrix tuples 矩阵元组的u不变量域
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-03-31 DOI: 10.13001/ela.2023.7355
A. Panov
{"title":"Fields of U-invariants of matrix tuples","authors":"A. Panov","doi":"10.13001/ela.2023.7355","DOIUrl":"https://doi.org/10.13001/ela.2023.7355","url":null,"abstract":"The general linear group $mathrm{GL}(n)$ acts on the direct sum of $m$ copies of $mathrm{Mat}(n)$ by the adjoint action. The action of $mathrm{GL}(n)$ induces the action of the unitriangular subgroup $U$. We present the system of free generators of the field of $U$-invariants.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43264032","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
Linear maps that preserve parts of the spectrum on pairs of similar matrices 在相似矩阵对上保留部分频谱的线性映射
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-03-23 DOI: 10.13001/ela.2023.7583
C. Costara
{"title":"Linear maps that preserve parts of the spectrum on pairs of similar matrices","authors":"C. Costara","doi":"10.13001/ela.2023.7583","DOIUrl":"https://doi.org/10.13001/ela.2023.7583","url":null,"abstract":"In this paper, we characterize linear bijective maps $varphi$ on the space of all $n times n$ matrices over an algebraically closed field $mathbb{F}$ having the property that the spectrum of $varphi (A)$ and $varphi (B)$ have at least one common eigenvalue for each similar matrices $A$ and $B$. Using this result, we characterize linear bijective maps having the property that the spectrum of $varphi (A)$ and $varphi (B)$ have common elements for each matrices $A$ and $B$ having the same spectrum. As a corollary, we also characterize linear bijective maps preserving the equality of the spectrum.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48077907","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
Positive and negative square energies of graphs 图的正能量和负能量平方
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-03-21 DOI: 10.13001/ela.2023.7827
A. Abiad, L. de Lima, Dheer Noal Desai, Krystal Guo, L. Hogben, Jos'e Madrid
{"title":"Positive and negative square energies of graphs","authors":"A. Abiad, L. de Lima, Dheer Noal Desai, Krystal Guo, L. Hogben, Jos'e Madrid","doi":"10.13001/ela.2023.7827","DOIUrl":"https://doi.org/10.13001/ela.2023.7827","url":null,"abstract":"The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Let $s^+(G), s^-(G)$ denote the sum of the squares of the positive and negative eigenvalues of $G$, respectively. It was conjectured by [Elphick, Farber, Goldberg, Wocjan, Discrete Math. (2016)] that if $G$ is a connected graph of order $n$, then $s^+(G)geq n-1$ and $s^-(G) geq n-1$. In this paper, we show partial results towards this conjecture. In particular, numerous structural results that may help in proving the conjecture are derived, including the effect of various graph operations. These are then used to establish the conjecture for several graph classes, including graphs with certain fraction of positive eigenvalues and unicyclic graphs.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47441495","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: 2
The inverse Horn problem 霍恩逆问题
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-03-01 DOI: 10.13001/ela.2023.7539
J. Queiró, A. P. Santana
{"title":"The inverse Horn problem","authors":"J. Queiró, A. P. Santana","doi":"10.13001/ela.2023.7539","DOIUrl":"https://doi.org/10.13001/ela.2023.7539","url":null,"abstract":"Alfred Horn's conjecture on eigenvalues of sums of Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an          $n$-tuple $gamma$ in the solution polytope, constructing Hermitian matrices with the required spectra such that their sum has eigenvalues $gamma$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46228169","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 permanent inequality for positive semidefinite matrices 正半定矩阵的一个永久不等式
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-02-24 DOI: 10.13001/ela.2023.7701
Vehbi E. Paksoy
{"title":"A permanent inequality for positive semidefinite matrices","authors":"Vehbi E. Paksoy","doi":"10.13001/ela.2023.7701","DOIUrl":"https://doi.org/10.13001/ela.2023.7701","url":null,"abstract":"In this paper, we prove an inequality involving the permanent of a positive semidefinite matrix and its leading submatrices. We obtain a result in the similar spirit of Bapat-Sunder per-max conjecture.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46162923","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 maximum spectral radius of graphs with a large core 具有大核的图的最大谱半径
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-02-24 DOI: 10.13001/ela.2023.7283
Xiaocong He, Lihua Feng, D. Stevanović
{"title":"The maximum spectral radius of graphs with a large core","authors":"Xiaocong He, Lihua Feng, D. Stevanović","doi":"10.13001/ela.2023.7283","DOIUrl":"https://doi.org/10.13001/ela.2023.7283","url":null,"abstract":"The $(k+1)$-core of a graph $G$, denoted by $C_{k+1}(G)$, is the subgraph obtained by repeatedly removing any vertex of degree less than or equal to $k$. $C_{k+1}(G)$ is the unique induced subgraph of minimum degree larger than $k$ with a maximum number of vertices. For $1leq kleq mleq n$, we denote $R_{n, k, m}=K_kvee(K_{m-k}cup {I_{n-m}})$. In this paper, we prove that $R_{n, k, m}$ obtains the maximum spectral radius and signless Laplacian spectral radius among all $n$-vertex graphs whose $(k+1)$-core has at most $m$ vertices. Our result extends a recent theorem proved by Nikiforov [Electron. J. Linear Algebra, 27:250--257, 2014]. Moreover, we also present the bipartite version of our result.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47160286","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 Graham-Hoffman-Hosoya-type theorems for the exponential distance matrix 指数距离矩阵的graham - hoffman - hosoya型定理
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-02-10 DOI: 10.13001/ela.2023.7449
Z. Du, Rundan Xing
{"title":"The Graham-Hoffman-Hosoya-type theorems for the exponential distance matrix","authors":"Z. Du, Rundan Xing","doi":"10.13001/ela.2023.7449","DOIUrl":"https://doi.org/10.13001/ela.2023.7449","url":null,"abstract":"Let $G$ be a strongly connected digraph with vertex set ${v_1, v_2, dots, v_n}$. Denote by $D_{ij}$ the distance between vertices $v_i$ and $v_j$ in $G$. Two variant versions of the distance matrix were proposed by Yan and Yeh (Adv. Appl. Math.), and Bapat et al.  (Linear Algebra Appl.) independently, one is the $q$-distance matrix, and the other is the exponential distance matrix. Given a nonzero indeterminate $q$, the $q$-distance matrix $mathscr{D}_G=(mathscr{D}_{ij})_{ntimes n}$ of $G$ is defined as[mathscr{D}_{ij}=left{begin{array}{cl}1+q+dots+q^{D_{ij}-1}&text{if $ine j$},0&text{otherwise}.end{array}right.]In particular, when $q = 1$, it would be reduced to the distance matrix of $G$. The exponential distance matrix $mathscr{F}_G=(mathscr{F}_{ij})_{ntimes n}$ of $G$ is defined as[mathscr{F}_{ij}= q^{D_{ij}}.] In $1977$, Graham et al.  (J. Graph Theory) established a classical formula connecting the determinants and cofactor sums of the distance matrices of strongly connected digraphs in terms of their blocks, which plays a powerful role in the subsequent researches on the determinants of distance matrices. Sivasubramanian (Electron. J. Combin.) and Li  et al. (Discuss. Math. Graph Theory) independently extended it from the distance matrix to the $q$-distance matrix. In this note, three formulae of such types for the exponential distance matrices of strongly connected digraphs will be presented.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41614980","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
Flat portions on the boundary of the numerical range of a 5 × 5 companion matrix 5伴随矩阵数值范围边界上的平坦部分
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-02-09 DOI: 10.13001/ela.2023.7209
Swastika Saha Mondal, Sarita Ojha, R. Birbonshi
{"title":"Flat portions on the boundary of the numerical range of a 5 × 5 companion matrix","authors":"Swastika Saha Mondal, Sarita Ojha, R. Birbonshi","doi":"10.13001/ela.2023.7209","DOIUrl":"https://doi.org/10.13001/ela.2023.7209","url":null,"abstract":"The number of flat portions on the boundary of the numerical range of $5 times 5$ companion matrices, both unitarily reducible and unitarily irreducible cases, is examined. The complete characterization on the number of flat portions of a $5 times 5$ unitarily reducible companion matrix is given. Also under some suitable conditions, it is shown that a unitarily irreducible $5 times 5$ companion matrix cannot have four flat portions on the boundary of its numerical range. This gives a partial affirmative answer to the conjecture given in [3] for $n = 5$. Numerical examples are provided to illustrate the results.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49036387","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: 2
Minimal rank weak Drazin inverses: a class of outer inverses with prescribed range 极小秩弱Drazin逆：一类具有指定范围的外逆
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-02-09 DOI: 10.13001/ela.2023.7359
Cang Wu, Jianlong Chen
{"title":"Minimal rank weak Drazin inverses: a class of outer inverses with prescribed range","authors":"Cang Wu, Jianlong Chen","doi":"10.13001/ela.2023.7359","DOIUrl":"https://doi.org/10.13001/ela.2023.7359","url":null,"abstract":"For any square matrix $A$, it is proved that minimal rank weak Drazin inverses (Campbell and Meyer, 1978) of $A$ coincide with outer inverses of $A$ with range $mathcal{R}(A^{k})$, where $k$ is the index of $A$. It is shown that the minimal rank weak Drazin inverse behaves very much like the Drazin inverse, and many generalized inverses such as the core-EP inverse and the DMP inverse are its special cases.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47028513","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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