Local(α,β)-Diagonally Dominant Matrix With a Nonzero Elements Chain

The concepts of local(α,β)-diagonally dominant matrix were introduced.Under the condition of local(α,β)-diagonally dominant matrix with a nonzero elements chain,by constructing a positive diagonal matrix X,the conclusion that B=AX was α-diagonally dominant matrix with a nonzero elements chain was presented,and a criterion for nonsingular H-matrix was obtained.The outcome implies that the extended local(α,β)-diagonally dominant concept is a development for matrix's diagonally dominance's theory,and a strong tool for researching H-matrix and M-matrix.