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关于矩阵方程AXB=C 总被引:1,自引:0,他引:1
关于矩阵方程AXB=C丁永臻(胜利油田师专数学系257097)文[1]给出了矩阵方程AXB=C有解和有唯一解的一个充要条件.本文借助于近代数学常用的矩阵广义逆、直积和拉直化运算的概念及性质详细讨论矩阵方程AXB=C解的一般理论,包括解的存在性、唯一性... 相似文献
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矩阵方程AX=B的实部正定解 总被引:2,自引:0,他引:2
本文主要讨论了矩阵方程AX=B(其中A,B∈Cm×n)的实部正定解的存在性,并在矩阵方程AX=B有实部正定解时,给出了通解的表达式. 相似文献
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在前期研究的基础上,对错误矩阵的概念作一个介绍,在此基础上,研究模糊错误矩阵方程的类型,且对于矩阵的每一行又恰好是一个模糊错误逻辑命题这种类型的模糊错误矩阵方程求解,由研究发现XA′的运算结果可得到A x′_1的运算结果等同于Ax′_1=A∧[x′_1,x′_1,…,x′_1]′,所以XAB模糊错误矩阵集合方程XA′=B的求解的方法可以得到改善.最后给出了一个求解的例子. 相似文献
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在前期研究的基础上,对错误矩阵的概念作一个介绍,在此基础上,且对于矩阵的每一行又恰好是一个模糊错误逻辑命题.因为构成这类模糊错误矩阵的元素是集合,所以这类模糊错误矩阵之间一般是集合关系式,而不只是通常方程的等式,研究这一类模糊错误矩阵方程解的存在性,求解的方法等是理论与实践的需要.以XA■B研究对象,研究得到模糊错误矩阵集合方程XA′=B解的存在性及给出求解的例子. 相似文献
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最大-最小型关系方程已有许多学者进行过研究并给出一些解法,这些解法在应用中仍显得过于复杂.本文在文献[1]的基础上对最大-最小型关系方程的极小解的性质和特点进行了系统的研究,并对文献[1]提出的求解这类方程的图法和分枝法在理论上进行了补充和完善.研究表明,图法和分枝法是求解最大-最小型关系方程的有效方法. 相似文献
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Fuzzy关系方程已经广泛地应用于Fuzzy综合评判、Fuzzy控制等领域。本文通过直接比较Fuzzy关系方程的系数与常数的大小,给出一个判别所给的Fuzzy关系方程是否有解的行之有效的简便方法,并且在有解时还给出求其最大解、极小解及解集的方法。 相似文献
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Tong Song JIANG Mu Sheng WEI 《数学学报(英文版)》2005,21(3):483-490
This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A X B = C, characterizes the existence of a solution to the matrix equation, and derives closed-form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation X - AXB =C. 相似文献
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Up to now, how to solve a fuzzy relation equation in a complete Brouwerian lattice is still an open problem as Di Nola et al. point out. To this problem, the key problem is whether there exists a minimal element in the solution set when a fuzzy relation equation is solvable. In this paper, we first show that there is a minimal element in the solution set of a fuzzy relation equation AX=b (where A=(a1,a2,…,an) and b are known, and X=(x1,x2,…,xn)T is unknown) when its solution set is nonempty, and b has an irredundant finite join-decomposition. Further, we give the method to solve AX=b in a complete Brouwerian lattice under the same conditions. Finally, a method to solve a more general fuzzy relation equation in a complete Brouwerian lattice when its solution set is nonempty is also given under similar conditions. 相似文献
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Luo Cheng-Zhong 《Journal of Mathematical Analysis and Applications》1984,103(2):524-532
The largest element of the solution set of a fuzzy relation equation has been found by E. Sanchez (Inform. and Control30 (1976), 38–48) but the smallest element does not exist. It is difficult to expose the solution of the fuzzy relation equation. In the case of the determinate relation equations, complete consequences have been found by Wang Peizhuang and Yuan Meng (“Relation Equation and Relation Inequalities,” Selected papers on fuzzy subsets, Beijing Normal University, March 1980). In the case of the fuzzy relation equations, Wang and Yuan have given a class of special solutions which probably possesses some minimality characterizations. In this paper, the reachable solution set of the fuzzy relation equation is given. For the fuzzy relation equation on the finite sets, a neat and efficient method for solving it is given. 相似文献
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定义基于∨ - .运算的 Fuzzy矩阵 A的同解简化矩阵 ,利用 A的同解简化矩阵 A(1) 给出基于∨ - .运算的 Fuzzy矩阵方程的矩阵解法 ,并研究这类 Fuzzy矩阵方程的摄动问题。 相似文献
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本文讨论了从细杆的振动中提出的一类带阻尼项的拟线性双曲型方程的初边值问题的解在唯一性,利用已有的线性结果及动点定理结合能量估计建立了解的存在唯一性。 相似文献