Generalized strictly diagonally dominant matrix play an important role in matrix theory and real applications. 广义严格对角占优矩阵在矩阵理论和实际应用中具有重要的作用和意义。
DONG An-guo, YOU Zhao-yong.An iterative judgment of generalized diagonally dominant matrix [J ].Journal of Xi'an Highway University, 1998,18(2): 115-117. 董安国
In this paper, some sufficient conditions and a necessary condition for a matrix to be a generalized strictly diagonally dominant matrix is given. Some previous results are improved and generalized. 本文给出了广义严格对角占优矩阵的若干充分条件和必要条件，从而改进和推广了一些已有的结果.
The sufficient and necessary conditions for the complex square matrix to be a generalzed diagonally dominant matrices are given in the paper. 给出了复方阵为广义对角占优阵的一个充要条件，同时也给出了复方阵为广义对角占优阵的判别方法。
But it isn't easy to determine whether the matrix is or not generalized strictly diagonally dominant matrix in reality, especially for the large matrices. 但实际中对此类矩阵进行有效判别,尤其是对大型矩阵的判别,还存在许多困难。