共查询到19条相似文献,搜索用时 140 毫秒
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行(列)反对称矩阵的满秩分解和广义逆 总被引:2,自引:0,他引:2
本文研究了行(列)转置矩阵与行(列)反对称矩阵的性质.利用分块矩阵理论获得了许多新的结果,给出了行(列)反对称矩阵的满秩分解、秩分解和广义逆的公式及快速算法.它们可极大地减少行(列)反对称矩阵的满秩分解、秩分解和广义逆的计算量与存储量,并且不会丧失数值精度. 相似文献
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为了简化大型行(列)酉对称矩阵的QR分解,研究了行(列)酉对称矩阵的性质,获得了一些新的结果,给出了行(列)酉对称矩阵的QR分解的公式和快速算法,它们可极大地减少行(列)酉对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度.同时推广和丰富了邹红星等(2002)的研究内容,拓宽了实际应用领域的范围. 相似文献
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《数学的实践与认识》2017,(18)
通过对母矩阵进行奇异值分解的方法得到广义行(列)酉对称矩阵的奇异值分解进一步得到其Moore-penrose逆;用谱分解方法得到母矩阵的Moore-penrose逆,进一步得到广义行(列)酉对称矩阵的Moore-penrose逆. 相似文献
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提出Satty′s互反判断矩阵一致性调整的一种新的简易方法,并借助EXCEL电子表格的动态引用功能,实现了判断者在建立判断矩阵时可即时地进行一致性的互动式调整;不但改善了现有不合理的强制性调整方法,而且提供了一种有效辅助判断矩阵建立的途径.其中,借鉴欧式距离原理构造了"行和列偏离程度系数"来衡量一致性优化调整过程有效性,同时实现了权重向量相对于互反判断矩阵调整的灵敏度分析.最后通过一个具体实例演示方法的操作过程,并检验了其有效性. 相似文献
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利用方阵的Jordan分解与翻转矩阵等技巧,给出方阵A、B及其张量积A(○×)B性质间的关系. 相似文献
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本文给出了一般线性矩阵方程AmnXns=Bms,XmnAns=Bms,AmnXnsBst=Cmt的解的结构定理,并介绍了一种利用初等变换求解上述三类线性矩阵方程的方法. 相似文献
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本文证明了阶为n(n≥7)的布尔矩阵的行空间维数的一个缺断区间为〔2^n-2+2n-3+2^n-4+2^n-5+2^n-6+1,2^n+1-1〕。这一结论扩展了关于布尔矩阵半群缺断区间的几个已有结果。作为应用,得到了布尔矩阵半群中一类偏序集的高度的一个新的上界,此外,还得到了关于有限拓扑维数分布的几个新结果。 相似文献
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拟次酉阵与拟次Hermite阵 总被引:4,自引:0,他引:4
提出了拟次酉阵、拟(反)次Hermite阵概念,研究了它们的性质及其相互间的关系,将正交矩阵广义Gayley分解推广到拟次酉阵上。 相似文献
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The problem of fast computing the QR factorization of row or column symmetric matrix is considered. We address two new algorithms based on a correspondence of Q and R matrices between the row or column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, for a class of row or column symmetric matrices, the QR factorization using the mother matrix rather than the row or column symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision. 相似文献
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Manfred Mö ller Franciszek Hugon Szafraniec 《Proceedings of the American Mathematical Society》2008,136(6):2165-2176
In this paper we discuss diverse aspects of the mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize the behaviour of row and column operators as they turn out to be the germs of an arbitrary matrix operator, providing most of the information about the latter as it is the troublemaker.
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J. N Singh D Singh 《International Journal of Mathematical Education in Science & Technology》2013,44(3):405-423
The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with infeasible interior methods and homogeneous self-dual methods for linear programming. Also discussed are some theoretical issues in interior-point methods like dependence of complexity bounds on some non-traditional measures different from the input length L of the problem. Finally, the paper concludes with remarks on the comparison of interior-point methods with the simplex method based on their performance on NITLIB suite, a standard collection of test problems. 相似文献
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Junjie Huang Junfeng Sun Alatancang Chen Carsten Trunk 《Mathematische Nachrichten》2019,292(11):2411-2426
Properties of right invertible row operators, i.e., of 1 × 2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2 × 2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated. 相似文献