四元数体上重行列式的性质及其应用

本文得到了四元数体上重行列式的一些基本不等式，给出了矩阵为正定自共轭阵时，行列式与重行列式的显式关系，同时也给出了文［１］中行列式与文［５］中行列式两种定义的关系。提出了四元数体上广义正定自共轭阵的概念，并获得了这类阵的基本性质．

Properties of Double Determinant over the Quaternion Field and Its Applicat ions

This paper gets inequalities on double determinant over the quaternion field. Forexample,the Minkowski’s inequality and convexity inequality of double determinant and so on.It gives the relation between the determinant and the double determinant, as well as the relationbetween the two kinds of definition of the determinant respectively in the paper 1] and paper4],if matrlx is the positive selfconjugate。 It puts forth the concept of generalization positiveselfconjugate matrix over the quaternion field and gets some of its basic properties.