Several properties of trace dominant matrix and generalized trace dominant matrix are obtained based on the concepts of trace dominant matrix and generalized trace dominant matrix.

Several properties of trace dominant matrix and generalized trace dominant matrix are obtained based on the concepts of trace dominant matrix and generalized trace dominant matrix.

Some new necessary and sufficient conditions for the complex square matrix to be a generalized dominant matrices are given in the paper.

α-diagonally dominant matrices andcriteria for generalized strictly diagonally dominant matrix;

A is a generalized strictly diagonally dominant matrix,both Jacobi and Gauss-Seidel iterative methods of Equation Ax=b converge.

We present some simple practical criteria for verifying whether a locally diagonally dominant matrix is a generalized strictly diagonally dominant matrix.

The concept of local double diagonally matrix is introduced in this paper,and three sufficient conditions of the generalized sub-diagonally dominant matrices are obtained.

A simple and practicable method of judging generalized strictly diagonally dominant matrices and nonsingular M-matrices is introduced.

In this paper, we adopt the definition of generalized Nekrasov matrices and give two equivalent conditions for generalized strictly diagonally dominant matrices, obtain some new practical criteria for generalized strictly diagonally dominant matrices, which include and extend some relevant results.

<Abstrcat>By using the properties of Ostrowski diagonally dominant matrix,some sufficient conditions for weak α-double diagonally dominant matrix to be generalized strictly diagonally dominant matrices and comparative matrices to be nonsingular M-matrices.