In this paper we propose the concept of a weak strictly diagonally dominant matrix given some DE terminate sufficient conditions for generalized strictly diagonally dominant matrices.

The calculation methods of diagonally dominant matrix in-situ replacement are researched, including the matrix determinant, the matrix equation unknown and the matrix inversion computation.

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.