UPPER BOUNDS FOR DETERMINANTS OF THE POSITIVEDEFINITE HERMITIAN MATRICES AND AN IMPROVEMENT OF HADANARD INEQUALITY
Tu Boxun(Mathematics Department)
This paper provided an improved inequality on upper bounds for the determinant of the positivedefinite Hermitian matrix. By using this inequality, an improvement of the famous Hadanard inequality on the upper bound of the determinant of any nonsingular matrix is given. This paper also represents some new results on upper bounds for the determinants of nonnormal matrices.