逆M-矩阵与正定矩阵Hadamard乘积行列式的下界

The Lower Bound of the Determinant for Hadamard Product of an Inverse M-matrix and a Positive Definite Matrix

首先改进了用于实对称正定矩阵的Hadamard乘积的行列式的下界估计的经典的Oppenheim不等式的加强形式,然后应用这个结论和逆M-矩阵的性质,得到了实对称正定矩阵和逆M-矩阵的Hadamard乘积的行列式的新下界估计。

Firstly, we improve the strengthened form of classical Oppenheim type inequality which plays a role in estimating the lower bound of the determinant for Hadamard product of real symmetric positive definite matrices. Secondly, making use of the result and the properties of inverse M-matrix, we obtain a new estimation on the lower bound of the determinant for Hadamard product of a real symmetric positive definite matrix and an inverse M-matrix.