复正定矩阵与复矩阵的和的行列式不等式

Inequalities on the Determinant of the Sum of a Complex Positive Definite Matrix and a Complex Matrix

讨论了复正定矩阵与复矩阵在一定条件下的和的行列式不等式,给出复正定矩阵的行列式的模的上、下界.所得结论是金(数学的实践与认识,2000,10:501～507.)和袁(数学研究与评论,2001,8:464～468.)关于复正定矩阵行列式上的不等式的推广.

In this paper, inequalities on the determinant of the sum of a complex positive difinite matrix and a complex matrix is discussed. We give upper and lower bounds for the norm of the determinant of the complex positive difinite matrix. And some known results on the determinant inequalities of complex matrices obtained by Jin (J Math Research and Exposition,2000,10:501～507.) and Yuan (Math Practice and Theory,2001,8:464～468.) are generalized.