复次亚正定矩阵的几个行列式不等式

On Determinant Inequalities in Complex Metapositive Sub-definite Matrix

在给出次亚正定矩阵和复次亚正定矩阵的概念和判定条件后,根据复次亚正定矩阵和次亚正定矩阵之间的关系,可利用次亚正定矩阵的行列式不等式推导出有关于复次亚正定矩阵的行列式不等式。可对复次亚正定矩阵涉及到的行列式不等式问题,复次亚正定矩阵的偏序问题进行探索,对所得结论,用实例予以说明和论证。

After the concept and sufficient criteria of metapositive subdefinite matrix and complex metapositive sub-definite matrix are presented, according to their relationship, complex metapositive sub-definite matrix determinant inequalities can be deduced from several determinant inequalities of metapositive subdefinite matrices. This paper probes into the determinant inequalities and parial order, then exemplifying and verifying its results.