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线性代数与矩阵理论研究进展(英文)最新文献

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Gradient-Based Iterative Algorithm for a Coupled Complex Conjugate and Transpose Matrix Equations 基于梯度的复共轭矩阵与转置矩阵耦合迭代算法
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-08-18 DOI: 10.4236/alamt.2021.113007
H. Yin, Huamin Zhang
{"title":"Gradient-Based Iterative Algorithm for a Coupled Complex Conjugate and Transpose Matrix Equations","authors":"H. Yin, Huamin Zhang","doi":"10.4236/alamt.2021.113007","DOIUrl":"https://doi.org/10.4236/alamt.2021.113007","url":null,"abstract":"Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90558646","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
Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms 次乘法矩阵范数的Fiedler和稀疏伴矩阵多项式根的界
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-02-23 DOI: 10.4236/ALAMT.2021.111001
Mamoudou Amadou Bondabou, Ousmane Moussa Tessa, Amidou Morou
{"title":"Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms","authors":"Mamoudou Amadou Bondabou, Ousmane Moussa Tessa, Amidou Morou","doi":"10.4236/ALAMT.2021.111001","DOIUrl":"https://doi.org/10.4236/ALAMT.2021.111001","url":null,"abstract":"We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88149882","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
A Note on SK, SK1, SK2 Indices of Interval Weighted Graphs 区间加权图的SK、SK1、SK2指标的注记
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-02-23 DOI: 10.4236/ALAMT.2021.111002
Semiha Başdaş Nurkahlı, S. Büyükköse
{"title":"A Note on SK, SK1, SK2 Indices of Interval Weighted Graphs","authors":"Semiha Başdaş Nurkahlı, S. Büyükköse","doi":"10.4236/ALAMT.2021.111002","DOIUrl":"https://doi.org/10.4236/ALAMT.2021.111002","url":null,"abstract":"In this study, the SK, SK1 and SK2 indices are defined on weighted graphs. Then, the SK, SK1 and SK2 indices are defined on interval weighted graphs. Their behaviors are investigated under some graph operations by using these definitions.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85710610","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
Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind 第三类Fredholm-Stiltjes线性积分方程解的唯一性
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-01-01 DOI: 10.4236/alamt.2021.114008
Aizat Toigonbaeva, A. Asanov, A. Kambarova, G. Obodoeva, U. Moldoyarov, A. Toktorbaev, Aichurok Abdukadyr Kyzy, Zhypargul D. Abdullaeva
{"title":"Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind","authors":"Aizat Toigonbaeva, A. Asanov, A. Kambarova, G. Obodoeva, U. Moldoyarov, A. Toktorbaev, Aichurok Abdukadyr Kyzy, Zhypargul D. Abdullaeva","doi":"10.4236/alamt.2021.114008","DOIUrl":"https://doi.org/10.4236/alamt.2021.114008","url":null,"abstract":"Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75296263","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
Unraveling Matrices 解开矩阵
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-01-01 DOI: 10.1007/978-3-030-52811-9_3
N. Johnston
{"title":"Unraveling Matrices","authors":"N. Johnston","doi":"10.1007/978-3-030-52811-9_3","DOIUrl":"https://doi.org/10.1007/978-3-030-52811-9_3","url":null,"abstract":"","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88682676","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
Matrix Decompositions 矩阵分解
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-01-01 DOI: 10.1007/978-3-030-52815-7_2
N. Johnston
{"title":"Matrix Decompositions","authors":"N. Johnston","doi":"10.1007/978-3-030-52815-7_2","DOIUrl":"https://doi.org/10.1007/978-3-030-52815-7_2","url":null,"abstract":"","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75519781","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
Representations of Lie Groups 李群的表示
线性代数与矩阵理论研究进展(英文) Pub Date : 2021-01-01 DOI: 10.4236/alamt.2021.114009
Amor Hasić
{"title":"Representations of Lie Groups","authors":"Amor Hasić","doi":"10.4236/alamt.2021.114009","DOIUrl":"https://doi.org/10.4236/alamt.2021.114009","url":null,"abstract":"In this paper, the most important liner groups are classified. Those that we often have the opportunity to meet when studying linear groups as well as their application in left groups. In addition to the introductory part, we have general linear groups, special linear groups, octagonal groups, symplicit groups, cyclic groups, dihedral groups: generators and relations. The paper is summarized with brief deficits, examples and evidence as well as several problems. When you ask why this paper, I will just say that it is one of the ways I contribute to the community and try to be a part of this little world of science.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82660281","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: 45
An Introduction to Lie Groups 李群导论
线性代数与矩阵理论研究进展(英文) Pub Date : 2020-11-26 DOI: 10.4236/alamt.2020.103004
Amor Hasić
{"title":"An Introduction to Lie Groups","authors":"Amor Hasić","doi":"10.4236/alamt.2020.103004","DOIUrl":"https://doi.org/10.4236/alamt.2020.103004","url":null,"abstract":"This paper is made out of necessity as a doctoral student taking the exam from Lie groups. Using the literature suggested to me by the professor, I felt the need to, in addition to that literature, and since there was more superficial in that book with some remarks about the examples given in relation to the left group. I decided to try a little harder and collect as much literature as possible, both for the needs of me and the others who will take after me. Searching for literature in my mother tongue I could not find anything, in English as someone who comes from a small country like Montenegro, all I could find was through the internet. I decided to gather what I could find from the literature in my own way and to my observation and make this kind of work. The main content of this paper is to present the Lie group in the simplest way. Before and before I started writing or collecting about Lie groups, it was necessary to say something about groups and subgroups that are taught in basic studies in algebra. In them I cited several deficits and an example. The following content of the paper is related to Lie groups primarily concerning the definition of examples such as The General Linear Group GL(n, R), The Complex General Linear Group GL(n, C), The Special Linear Group SL(n, R)=SL(V), The Complex Special Linear Group SL(n, C), Unitary and Orthogonal Groups, Symplectic Group, The groups R*, C*, S1 and Rn and others. In addition, invariant vector fields and the exponential map and the lie algebra of a lie group. For me, this work has the significance of being useful to all who need it.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85121694","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
The Equivalence between Orthogonal Iterations and Alternating Least Squares 正交迭代与交替最小二乘的等价性
线性代数与矩阵理论研究进展(英文) Pub Date : 2020-04-30 DOI: 10.4236/alamt.2020.102002
A. Dax
{"title":"The Equivalence between Orthogonal Iterations and Alternating Least Squares","authors":"A. Dax","doi":"10.4236/alamt.2020.102002","DOIUrl":"https://doi.org/10.4236/alamt.2020.102002","url":null,"abstract":"This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank-k approximation of a real m×n matrix, A. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, G, this method computes k dominant eigenvectors of G. To see the relation between these methods we assume that G = AT A. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75958157","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
Linear Codes over the Finite Ring Z15 有限环Z15上的线性码
线性代数与矩阵理论研究进展(英文) Pub Date : 2020-04-08 DOI: 10.4236/alamt.2020.101001
Wen-sheng Li, Lingyu Wan, Meng-tian Yue, Wei Chen, Xuedong Zhang
{"title":"Linear Codes over the Finite Ring Z15","authors":"Wen-sheng Li, Lingyu Wan, Meng-tian Yue, Wei Chen, Xuedong Zhang","doi":"10.4236/alamt.2020.101001","DOIUrl":"https://doi.org/10.4236/alamt.2020.101001","url":null,"abstract":"In this paper, the structure of the non-chain ring Z15 is studied. The ideals of the ring Z15 are obtained through its non-units and the Lee weights of elements in Z15 are presented. On this basis, by the Chinese Remainder Theorem, we construct a unique expression of an element in Z15. Further, the Gray mapping from Zn15 to Z2n15 is defined and it’s shown to be distance preserved. The relationship between the minimum Lee weight and the minimum Hamming weight of the linear code over the ring Z15 is also obtained and we prove that the Gray map of the linear code over the ring Z15 is also linear.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77452912","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
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