Abstract: To determine a given matrix is a  nonsingular $H$-matrix or not plays an important role in mathematical economics, control theory, and so on. To get more nonsingular $H$-matrices easily, several practical sufficient conditions for nonsingular $H$-matrices  are  obtained by constructing exquisite positive diagonal matrices and applying some technical of inequalities. The corresponding results are improved and extended. Advantages of these results are illustrated by a numerical example.

Key words: nonsingular $H$-matrices, generalized Nekrasov matrices, strictly generalized diagonally dominant matrices, irreducibility, nonzero elements chain