极大加代数矩阵的整特征向量

Integer Eigenvectors of Max-plus Matrices

本文研究极大加代数矩阵的整特征向量.提出块整特征向量的概念,分别给出可约矩阵存在块整特征向量的充分必要条件和在一定条件下存在整特征向量的充分必要条件.提出广义整像算法,通过验证主对角线上的块矩阵确定矩阵(可约和不可约矩阵)的整特征向量.数值例子表明广义整像算法是伪多项式算法.

Integer eigenvector of max-plus matrices is considered in this paper. The concept of block integer eigenvector is introduced and the necessary and sufficient conditions of existing block integer eigenvector and existing integer eigenvector under certain conditions of reducible matrix are presented, respectively. The general INT-IMAGE algorithm is given which can apply to irreducible and reducible matrices and is used to determine the integer eigenvector by verifying the integer image of block matrices on the main diagonal line. Numerical example shows that the general INT-IMAGE algorithm is a pseudo-polynomial algorithm.