实四元数矩阵行列式一个不等式及其应用

An Ineguality on Determinant of Real Quaternions Matrices and its Applications

本文将实矩阵行列式的Taussky不等式推广实四元数矩阵上,并给出了其在四元数方阵非奇判定上的某些应用。

In this paper we prove an ineguality on determinant of real guate-rnions matrices and point out some use in criterions of nonsingularity of real quaternions square matrices. Main result: Suppose A, B are real quaternions matrices and'A>0, B=-B.then N( et(A + B))>N( etA)= ||A||2, where etA and ||A|| are Dieudonne de-terminant[1] and Xie Bangjie determinant[2] If A + B is also the centralizable,