共查询到20条相似文献,搜索用时 78 毫秒
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关于多个子空间的交空间与维数公式的推广 总被引:1,自引:1,他引:0
通过讨论,得到了关于多个子空间的交空间的进一步的结果.并利用这些结果,给出了维数公式的一个新的推广形式,从而完善了维数公式的理论. 相似文献
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苏哲斌 《数学的实践与认识》2009,39(10)
研究了三角模糊数互反和互补判断矩阵的相互转换和一致性问题.提出了三角模糊数互反判断矩阵完全一致性的定义以及三角模糊数互补判断矩阵加性一致性和乘性一致性的定义,给出了两类模糊数判断矩阵相互转化的公式,论证了转换公式对判断矩阵一致性的保持关系.最后,基于一致性模糊数判断矩阵元素和排序权值的关系,建立了两个方案排序的非线性规划模型. 相似文献
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由两个模糊数的隶属函数确定三个面积,据此建立一个对模糊数进行大小比较的可能度计算公式.公式表达式非常简洁,同时还具有传递性、互补性等诸多良好的性质,因而具有很强的实用性和可操作性.对给定的一组模糊数,先利用两两比较的结果建立一个可能度矩阵,同时给出基于可能度矩阵的模糊数排序算法.最后给出一个排序算法的实例. 相似文献
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苏哲斌 《数学的实践与认识》2010,40(9)
研究了三角模糊数判断矩阵的排序问题,在两个三角模糊数相互比较大小的可能度的基础上,综合分析直接和间接两个方面的比较因素,提出了两个三角模糊数比较的优势度概念.对三角模糊数判断矩阵的行元素信息进行集结并利用所定义的优势度概念作为度量对集结的结果两两进行比较,构造出相应的以实数表示的模糊互补优势度矩阵,进而利用模糊互补判断矩阵的排序公式得到方案的排序权值.最后通过一个算例说明了提出的排序方法. 相似文献
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基于一致性逼近的三角模糊数互补判断矩阵的排序方法 总被引:1,自引:0,他引:1
研究了元素为三角模糊数形式的互补判断矩阵的一致性和排序问题.分析了三角模糊数互补判断矩阵和三角模糊数互反判断矩阵之间的相互转换关系,提出了这两类判断矩阵完全一致性的概念并得到了三角模糊数互补判断矩阵的元素和排序权值之间的关系,在此基础上建立了一个多目标优化模型,通过求解该模型得到三角模糊数互补判断矩阵的排序向量,利用已有的模糊数比较大小公式得到方案的排序,最后给出了一个算例. 相似文献
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研究了属性值以区间数表示的群决策问题,提出了区间数决策向量转化为互反判断矩阵的公式,定义了区间数互反判断矩阵几何加权集成算子.在此基础上,提出了区间数多属性群决策的新方法.方法首先针对每一个属性,将各决策者、各方案对应此属性的区间数向量转换为互反判断矩阵,由新定义的集成算子进行集成.由集成区间数矩阵的上界、下界矩阵计算各方案关于此属性的排序向量.由属性权重、可能度和排序公式对方案进行排序.最后给出一个实例进行分析,结果表明了此方法的实用性和可行性. 相似文献
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《数学的实践与认识》2013,(24)
讨论了一类高阶矩阵差分方程的解及渐近稳定性问题.利用特征子空间的维数得到了特征方程存在可对角化解的一个充要条件;然后利用特征方程的相异解刻划出该矩阵差分方程的通解,并给出其解渐近稳定的两个充分条件.推广了相关文献的结果. 相似文献
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Zoran Z. Petrovi? 《Linear algebra and its applications》2009,431(8):1199-1207
In this paper we investigate the maximal dimension for k-spaces of real matrices for small values of k. We also give some bounds for the dimension of spaces of real matrices of high rank. 相似文献
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The G-orthogonal matrices, defined in this paper, have, unlike orthogonal and Lorentz matrices, complex eigenvalues of modulus not equal to 1, and a corresponding invariant subspace of dimension four. They can be expressed as the exponential of some canonical matrix. 相似文献
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We examine combinatorial properties of extremal plane stochastic matrices of dimension three. Methods are given for the construction of such extremal matrices of any order. We obtain a lower bound for the number of connected extremal matrices of order n and conclude with some open problems. 相似文献
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ABSTRACTIn this paper, we study a particular class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. As applications, we first present a technique from which we can get closed formulas for the roots of many families of polynomial equations with degree between 5 and 10, inclusive. Then, we describe a tool that shows how to find solutions to Fermat's last theorem and Beal's conjecture over the square integer matrices of any dimension. Finally, simple generalizations of some of the concepts in number theory to integer square matrices are presented. 相似文献
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The concept of a strictly positive definite set of Hermitian matrices is introduced. It is shown that a strictly positive definite set is always a positive definite set, and conditions are found under which a positive definite set is strictly positive definite. We also show that a set of Hermitian matrices is strictly positive definite if and only if some nonnegative linear combination of these matrices is a positive definite matrix. For state dimension two, we use this concept to find necessary and sufficient conditions for a two-mode completely controllable irreducible multimodal system to be contractible relative to an elliptic norm. For general state dimensions, we give necessary and sufficient conditions for a special-type two-mode completely controllable irreducible system to be contractible relative to a weakly monotone norm. Applying the above results, we show that, for state dimension two, there exists a completely controllable two-mode system which is not contractible relative to either an elliptic or a weakly monotone norm. We leave open the question whether or not complete controllability implies contractibility, relative to some norm, for multimodal systems of two or more modes. 相似文献
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《Journal of Complexity》2005,21(4):609-650
The shifted number system is presented: a method for detecting and avoiding error producing carries during approximate computations with truncated expansions of rational numbers. Using the shifted number system the high-order lifting and integrality certification techniques of Storjohann 2003 for polynomial matrices are extended to the integer case. Las Vegas reductions to integer matrix multiplication are given for some problems involving integer matrices: the determinant and a solution of a linear system can be computed with about the same number of bit operations as required to multiply together two matrices having the same dimension and size of entries as the input matrix. The algorithms are space efficient. 相似文献
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We state and prove some characterizations of the topological dimension of compact metric spacesK by the matrices representingC(K) as a predual ofL 1(μ). 相似文献
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Hou-Biao Li Ting-Zhu Huang Hong Li 《Journal of Computational and Applied Mathematics》2010,234(10):2943-270
In this study, some upper and lower bounds for singular values of a general complex matrix are investigated, according to singularity and Wielandt’s lemma of matrices. Especially, some relationships between the singular values of the matrix A and its block norm matrix are established. Based on these relationships, one may obtain the effective estimates for the singular values of large matrices by using the lower dimension norm matrices. In addition, a small error in Piazza (2002) [G. Piazza, T. Politi, An upper bound for the condition number of a matrix in spectral norm, J. Comput. Appl. Math. 143 (1) (2002) 141-144] is also corrected. Some numerical experiments on saddle point problems show that these results are simple and sharp under suitable conditions. 相似文献