Abstract: To estimate the determinant of a matrix is a hot issue in numerical algebra. The class of $H$-matrices has a wide range of applications in many fields such as computational mathematics, control theory. In this paper, the estimations for determinants of Dashnic-Zusmanovich type matrices are studied. For a Dashnic-Zusmanovich type matrix, we transform it into a diagonally dominant matrix by using scaling matrices. Then we obtain the upper and lower bounds for the determinant of the Dashnic-Zusmanovich type matrix. Numerical examples are given to illustrate the effectiveness of the proposed results.

Key words: Nonsingular $H$-matrix ,  , Dashnic-Zusmanovich type matrix , Determinant