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MATRIX ALGEBRA ALGORITHM OF STRUCTURE RANDOM RESPONSE NUMERICAL CHARACTERISTICS 认领 引用
1
作者 Mei YulinWang XiaomingWang DelunDepartment of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China 《Chinese Journal of Mechanical Engineering》 EI CAS 2003年第2期149-152,共4页
A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can ... A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response. 展开更多
关键词 matrix algebra algorithm structure random response numericalcharacteristics numerical integration fast algorithm non-proportion damp
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An involutive Jordan automorphism of triangular matrix algebra over commutative rings 认领 引用
2
作者 王兴涛 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2005年第4期376-377,共2页
Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-alge... Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）. 展开更多
关键词 Jordan automorphism matrix algebra commutative ring
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Decomposition of Jordan automorphism of two-order upper triangular matrix algebra over certain semilocal rings 认领 引用
3
作者 王兴涛 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2006年第1期4-5,共2页
Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomp... Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms. 展开更多
关键词 Jordan automorphism upper triangular matrix algebra semilocal ring
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(m,n)-Igusa-Todorov Algebras,IT-Dimensions and Triangular Matrix Algebras 认领 引用 被引量：1
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作者 Jiyuan TANG Yuanfeng ZHANG Hanpeng GAO 《Journal of Mathematical Research with Applications》 CSCD 2024年第3期337-343,共7页
Let T,U be two Artin algebras andUMTbe a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov whenUM,MTare... Let T,U be two Artin algebras andUMTbe a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov whenUM,MTare projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}. 展开更多
关键词 Igusa-Todorov algebras IT-dimensions triangular matrix algebras
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Jordan Left Derivations of Generalized Matrix Algebras 认领 引用
5
作者 Li Chen-Fang Li Yan-Bo 《Communications in Mathematical Research》 CSCD 2014年第4期301-306,共6页
In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.
关键词 generalized Jordan left derivation Jordan left derivation generalized matrix algebra generalized left derivation
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TOPOLOGICAL AND GEOMETRIC PROPERTY OF MATRIX ALGEBRA 认领 引用
6
作者 Jipu Ma 《Analysis in Theory and Applications》 2007年第2期196-200,共5页
Let B（R^n） be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL（R^n） is a Lie group an... Let B（R^n） be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL（R^n） is a Lie group and also a smooth hypersurface in B（R^n） with the dimension n × n. 展开更多
关键词 matrix algebra acrwise connected component smooth hypersurface (submanifold) generalized inverse dimension of hypersurface
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Co-commuting Mappings of Generalized Matrix Algebras 认领 引用
7
作者 Liang Xin-feng Xiao Zhan-kui Du Xian-kun 《Communications in Mathematical Research》 CSCD 2015年第4期311-319,共9页
Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we ... Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper. 展开更多
关键词 co-commuting map generalized matrix algebra proper
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Perfect Matrix Algebras ∑(λ)(Ⅱ)-AK-Property 认领 引用
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作者 吴从炘 《Northeastern Mathematical Journal》 2001年第4期392-396,共5页
In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
关键词 perfect sequence space perfect matrix algebra AK-property row-AK-property column-AK-property
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One-to-One Map of Dirac Equation between Matrix Algebra and Geometric Algebra Cl3,0 认领 引用
9
作者 Jesús Sánchez 《Journal of Applied Mathematics and Physics》 2025年第9期2945-2975,共31页
In this paper,it is created a one-to-one map between the Dirac Equation in Matrix Algebra and the Dirac Equation in Geometric Algebra Cl3,0.The eight free parameters of the spinors in matrix representation correspond ... In this paper,it is created a one-to-one map between the Dirac Equation in Matrix Algebra and the Dirac Equation in Geometric Algebra Cl3,0.The eight free parameters of the spinors in matrix representation correspond to the coefficients of the eight elements of the Geometric Algebra Cl3,0(scalars,three vectors,three bivectors and the trivector).This way,a one-to-one mapping between matrix representation and Geometric Algebra Cl3,0 can be obtained. 展开更多
关键词 Geometric Algebra Matrix Algebra Dirac Equation Quantum Mechanics Wavefunction Basis Vectors
Representations of Frobenius-type Triangular Matrix Algebras 认领 引用 被引量：1
10
作者 Fang LI Chang YE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2017年第3期341-361,共21页
The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any ... The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices. 展开更多
关键词 Frobenius-type triangular matrix algebras reflection functor locally free module rootsystem APR-tilting module
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Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras 认领 引用 被引量：1
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作者 Yan Xia ZHAO Rui Ping YAO Deng Yin WANG 《Journal of Mathematical Research and Exposition》 2010年第3期465-474,共10页
Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and t... Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and that every local Jordan automorphism of Tn（R） is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of Tn （R） are inner. 展开更多
关键词 local Jordan derivations local Jordan automorphisms local derivations localautomorphisms upper triangular matrix algebras.
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Piecewise Hereditary Triangular Matrix Algebras 认领 引用
12
作者 Yiyu Li Ming Lu 《Algebra Colloquium》 SCIE CSCD 2021年第1期143-154,共12页
For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A ... For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A⊗K[X]/(XN)for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories. 展开更多
关键词 piecewise hereditary algebras triangular matrix algebras ^-complexes singularity categories Coxeter polynomials
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New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy 认领 引用 被引量：1
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作者 YU Fa-Jun ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS 2006年第4期587-592,共6页
A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A^-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville in... A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A^-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hicrarchy of soliton equations is generated, which possesses the multi.component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi.component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem. 展开更多
关键词 matrix Lie algebra Liouville integrable integrable coupling
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Product Zero Derivations on Strictly Upper Triangular Matrix Lie Algebras 认领 引用
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作者 Zhengxin CHEN Liling GUO 《Journal of Mathematical Research with Applications》 CSCD 2013年第5期528-542,共15页
Let F be a field, n ≥ 3, N（n,F） the strictly upper triangular matrix Lie algebra consisting of the n × n strictly upper triangular matrices and with the bracket operation {x, y} = xy-yx. A linear map φ on N（... Let F be a field, n ≥ 3, N（n,F） the strictly upper triangular matrix Lie algebra consisting of the n × n strictly upper triangular matrices and with the bracket operation {x, y} = xy-yx. A linear map φ on N（n,F） is said to be a product zero derivation if {φ（x）,y] ＋ [x, φ（y）] = 0 whenever {x, y} = 0,x,y ∈ N（n,F）. In this paper, we prove that a linear map on N（n, F） is a product zero derivation if and only if φ is a sum of an inner derivation, a diagonal derivation, an extremal product zero derivation, a central product zero derivation and a scalar multiplication map on N（n, F）. 展开更多
关键词 product zero derivations strictly upper triangular matrix Lie algebras derivations of Lie algebras.
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New Matrix Loop Algebra and Its Application 认领 引用
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作者 DONG Huan-He XU Yue-Cai 《Communications in Theoretical Physics》 SCIE CAS 2008年第8期321-325,共5页
A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of t... A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra. 展开更多
关键词 matrix loop algebra Liouville integrable system Hamiltonian structure integrable couplings
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Accurate calculation and Matlab based fast realization of merit function's Hesse matrix for the design of multilayer optical coating 认领 引用 被引量：10
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作者 吴素勇 龙兴武 杨开勇 《Optoelectronics Letters》 EI 2009年第5期359-363,共5页
To improve the current status of home multilayer optical coating design with low speed and poor efficiency when a large layer number occurs, the accurate calculation and fast realization of merit function＇s gradient ... To improve the current status of home multilayer optical coating design with low speed and poor efficiency when a large layer number occurs, the accurate calculation and fast realization of merit function＇s gradient and Hesse matrix is pointed out. Based on the matrix method to calculate the spectral properties of multilayer optical coating, an analytic model is established theoretically. And the corresponding accurate and fast computation is successfully achieved by programming with Matlab. Theoretical and simulated results indicate that this model is mathematically strict and accurate, and its maximal precision can reach floating-point operations in the computer, with short time and fast speed. Thus it is very suitable to improve the optimal search speed and efficiency of local optimization methods based on the derivatives of merit fimction. It has outstanding performance in multilayer optical coating design with a large layer number. 展开更多
关键词 MATLAB Matrix algebra Multilayers Optical beam splitters Optical coatings Optical materials Optical properties
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MATRIX PERTURBATION METHOD FOR THE VIBRATION PROBLEM OF STRUCTURES WITH INTERVAL PARAMETERS 认领 引用
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作者 邱志平 陈塑寰 刘中生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第6期551-560,共10页
When the parameters of structures are uncertain, the structural natural frequencies become uncertain. The interval parameters description, i.e. the unknown-but bounded parameters description is one of the methods to s... When the parameters of structures are uncertain, the structural natural frequencies become uncertain. The interval parameters description, i.e. the unknown-but bounded parameters description is one of the methods to study the uncertainty. In this paper, the vibration problem of structure with interval parameters was studied, and the eigenvalue problem of the structures with interval parameters was transferred into two different eigenvalue problems. The perturbation method was applied to the vibration problem of the structures with interval parameters. The numerical results show that the proposed method is sufficiently accurate and needs less computational efforts. 展开更多
关键词 Eigenvalues and eigenfunctions Matrix algebra Perturbation techniques Structural design
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An algorithm to solve autocorrelation matrix singular value based on SNR estimation 认领 引用
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作者 赵继军 张曙光 赵文玉 《Optoelectronics Letters》 EI 2009年第1期41-44,共4页
SNR estimation of communication signals is important to improve demodulation performance and channel quality of communication system,thus it is an important research issue of communication field.According to the core ... SNR estimation of communication signals is important to improve demodulation performance and channel quality of communication system,thus it is an important research issue of communication field.According to the core problem of autocorrelation matrix singular value in SNR estimation process,through making use of householder transforming autocorrelation matrix into tridiagonal matrix,and by using the relation of corresponding characteristic equation coefficients and singular value,a numerical algorithm is gi... 展开更多
关键词 Acoustic intensity Algorithms Channel estimation Communication systems Correlation detectors Estimation Matrix algebra
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知识再发现视角下实对称矩阵惯性定理的新证探究 认领 引用 被引量：1
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作者 王卿文 何卓衡 张扬 《纯粹数学与应用数学》 2026年第1期104-112,共9页
惯性定理作为线性代数的核心定理之一,是连接实对称矩阵、二次型与向量空间理论的关键纽带,其抽象性与严谨性给本科线性代数的研究与学习带来诸多难点.“知识再发现”范式强调以探究为核心,引导学生重历知识的生成、探究与完善过程,契... 惯性定理作为线性代数的核心定理之一,是连接实对称矩阵、二次型与向量空间理论的关键纽带,其抽象性与严谨性给本科线性代数的研究与学习带来诸多难点.“知识再发现”范式强调以探究为核心,引导学生重历知识的生成、探究与完善过程,契合线性代数抽象知识的研究与认知规律.本文以“知识再发现”为核心视角,结合分块矩阵工具,完整呈现惯性定理新证的全探究过程,依次展开“实例感知―猜想提出―逻辑验证―严谨论证―拓展延伸”的再发现路径,同步阐释该过程带来的数学研究思维、范式创新及能力培育层面的启发,实现“定理证明―探究过程―启发提炼”的有机统一,为线性代数抽象定理的研究提供全新范式参考与方法支撑. 展开更多
关键词 知识再发现 惯性定理 实对称矩阵 分块矩阵 线性代数研究
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灵活运用矩阵等式是学好线性代数的关键 认领 引用
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作者 杨威 樊松涛 《高等数学研究》 2026年第1期98-102,共5页
在线性代数课程中,一些基本概念可以用矩阵等式来定义,一些具体问题也可以用矩阵等式来描述;另一方面,从一个矩阵等式中往往可以挖掘出很多的线性代数含义.本文通过一些具体案例来说明矩阵等式在线性代数课程中的重要意义.
关键词 矩阵等式 线性代数 抽象思维能力
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