| 分配格上矩阵的特征向量 |
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| 引用本文： | 周惊雷,李庆国. 分配格上矩阵的特征向量[J]. 模糊系统与数学, 2007, 21(1): 36-41 |
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| 作者姓名： | 周惊雷 李庆国 |
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| 作者单位： | 湖南大学,数学与计量经济学院,湖南,长沙,410082;湖南文理学院,数学系,湖南,常德,415000;湖南大学,数学与计量经济学院,湖南,长沙,410082 |
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| 摘 要： | 设(L,≤,∨,∧)为一分配格。满足Ax=x的向量x称为方阵A的特征向量。本文的主工目的是通过矩阵的伴随有向图来刻画矩阵的特征向量并给出矩阵特征向量的界。同时我们将定义矩阵A的上基本特征向量并讨论它的性质。
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| 关 键 词： | 分配格 矩阵 特征向量 上基本特征向量 |
| 文章编号： | 1001-7402（2007）01-0036-06 |
| 收稿时间： | 2005-10-08 |
| 修稿时间： | 2005-10-08 |
On Eigenvectors of Matrices over Distributive Lattices |
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| ZHOU Jing-lei,LI Qing-guo. On Eigenvectors of Matrices over Distributive Lattices[J]. Fuzzy Systems and Mathematics, 2007, 21(1): 36-41 |
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| Authors: | ZHOU Jing-lei LI Qing-guo |
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| Affiliation: | 1. School of Mathematics and Econometrics,Hunan University,Changsha 410082,China; 2. Department of Mathematics,Hunan University of Arts and Science,Changsha 415000,China |
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| Abstract: | Let (L, ≤, ∨, ∧ ) be a distributive lattice. A vector x is said to be an eigenvector of a square matrix A over the lattice L if Ax = x. The aim of this paper is to characterize the eigenvectors by means of the associated graph of the matrix and to give the bounds for the set of all eigenvectors. We will define the upper basic eigenvector of the square matrix A over the lattice L and discuss the properties of it. |
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| Keywords: | Distributive lattice Matrix Eigenvector The Upper Basic Eigenvector |
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