极端U_1矩阵的充要条件

Necessary and sufficient conditions of an extreme U_1 matrix

相关文献最近在研究双随机算子和极端双随机算子的充要条件时,提出U1矩阵的概念,并成功地利用U1矩阵和极端U1矩阵的工具,取得丰硕的成果.这样一来,极端U1矩阵的进一步研究应该是有意义的.相关文献仅给出U1矩阵是极端U1矩阵的一个必要条件,作者进一步给出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.此外,还对有一个n-1阶主子矩阵是饱和的U1矩阵,给出它是极端U1矩阵的充要条件.

The concept of U1 matrix was initialized in other articles where a necessary condition for a U1 matrix to be extreme is given.In this paper,we present a necessary and sufficient condition for a U1 matrix to be extreme.Also we present a necessary and sufficient condition for a symmetric Nonnegative matrix to be an extreme U1 matrix.Finally,we give a necessery and sufficient condition for a U1 matrix,that possesses a saturated principal submatrix of order n-1,to be extreme U1 matrix.