块广义严格对角占优矩阵的判定准则

The Criteria for Block Generalized Strictly Diagonally Dominant Matrices

根据块广义对角占优矩阵研究中的实际困难,利用广义严格对角占优矩阵与块广义严格对角占优矩阵之间的关系,利用矩阵分块技术,对矩阵元素间的关系进行研究,利用其自身元素间的关系给出块广义严格对角占优矩阵的判定条件,并利用此结论给出判定矩阵是否可逆的充分条件.

In order to overcome the difficult of the method in practice for block generalize strictly diagonally dominant matrices,based on the connection of generalize strictly diagonal dominant matrices and block generalize strictly diagonally dominant matrices,a new simple criterion for block generalize strictly diagonally dominant matrices are obtained by making use of the norm of sub-matrices of a given matrix only. As an application,the sufficient conditions of inverse matrices are given.