Simple Criteria for Nonsingular H-Matrices

Some criterions and properties were presented for a matrix to be a nonsingular H-matrix using matrix's concepts of irreducibility, α-diagonally dominance and α-doubly diagonally dominance and the method of G-function and matrix's directed graph. In the meantime, the matrix's eigenwert and nonsingular problem was analyzed under the condition of irreducibility and diagonally dominance. The theory of α-doubly diagonally dominance and H-matrix was improved and enriched, which provided the theory's base for relative fields, such as in numerical analysis, matrix theory, control theory and mathematical economics.