块半正定矩阵Hadamard积的行列式不等式

Determinant Inequalities for Block Hadamard Product of Positive Semi-Definite Matrices

基于分块矩阵的Schur补和Albert定理,证明了一些含有块Hadamard积的行列式不等式,并且用不同于文献的方法证明了半正定Hermitian矩阵块Hadamard积的行列式不等式的一个猜想,此结果推广了半正定Hermitian矩阵在块Hadamard积下的Oppenheim不等式.

Based on Schur complements and Albert＇s theorem, in this short paper, we show several determinant inequalities involving block Hadamard product and prove a conjecture on matrix determinant inequality for block Hadamard product of positive semi-definite Hermi- tian matrix by the others way. Our results are the generalization of Oppenheim＇s inequality for block Hadamard product of positive semi-definite matrices.