非负矩阵的一些算法

本文利用有限图论和齐次有限马尔可夫链理论的有关命题和算法得到了不同于1]、3]的算法:(1)有限阶非负矩阵可约性的判别、有限阶可约矩阵化为主对角线上都为不可约子块的分块三角阵的算法;(2)有限阶不可约矩阵的Frobenius表示的算法.对上述二算法本文还分别给出了直观简便的图示法.

Some Algorithms of Nonnegative Matrices

By mcans of graph theory and homogeneous finite Markov Chain theory, the following are obtained.(1) An algorithm of test for reducibility of a finite nonnegative matrix and transforming a finite reducible matrix into block triangular form so that each of the diagonal blocks of the matrix is irreducible. (2) An algorithm transforming a finite irreducible matrix into Frobenius' form. The two algorithms and their proofs are simple and different from those of 1] and 3]. When the dimensions of the matrix is moderate, an intuitive and convenient graphic method is offered for each of the two algorithms.