Two Subsets of Nonsingular H-Matrix

The concept of local(α,β)-doubly diagonally dominant matrix was introduced.Under the conditions of strict local(α,β)-doubly diagonally dominant and irreducible local(α,β)-doubly diagonally dominant matrix,the conclusion that B=AX is a strict α-diagonally dominant matrix or irreducible α-diagonally dominant matrix was presented by constructing a suitable positive diagonal matrix X, for a given complex matrix A,thus two practical criterions of nonsingular Hmatrix were obtained.The results show that the extended local (α,β)-doubly diagonally dominant concept is a development for matrix's doubly diagonally dominance's theory and a powerful tool for researching of H-matrix and M-matrix.These conclusions not only promote the development of matrix's theory itself,but also provide strong basis for the research of relative fields such as computational mathematic,control theory,etc.