极端U_1矩阵的结构与计数

Construction and counting of extreme U_1 matrices

相关文献在研究单纯形上的双随机算子和极端双随机算子的充要条件时,成功地利用U1矩阵和极端U1矩阵的工具,取得丰硕成果.其在给出U1矩阵是极端U1矩阵的必要条件基础上,进一步给出U1矩阵是极端U1矩阵的充要条件及对称非负矩阵是极端U1矩阵的充要条件.论文继续深入研究极端U1矩阵的性质,包括其直和结构、置换相似类个数的计算和谱半径估计,并对相关文献提出的猜想给出肯定性的证明.

Some reference uses U 1 and extreme U1 matrices to investigate the necessary and sufficient condition for a quadratic operator defined on the simplex to be a quadratic stochastic operator or an extreme quadratic stochastic operator. Other reference presented a necessary and sufficient condition for a U1 matrix to be an extreme U1 matrix （ other reference only presented the necessary condition ） , and a necessary and sufficient condition for a symmetric nonnegative matrix was an extreme U1 matrix. In this paper, we continued to investigate extreme U1 matrices including the structure of an extreme U1 matrix , counted the number of n × n extreme U1 matrices and computed the spectral radius of an n × n extreme U1 matrix. Finally we proved the conjecture given in other articles.