广义四元数体上矩阵的最小多项式

The Minimal Polynomial of Matrix over the Generalized Quaternion Field

本文给出了广义四元数体上方阵的最小多项式与最小中心多项式的构造公式，讨论了它们的性质及其应用，得到广义四元数方阵相似于对角矩阵的一个充要条件。

This paper gives the structure formulas of the minimal polynomial and minimalcentral poiynomial of any nx n matrix over the generalized quaternion field,discusses their someproperties and applications,and obtalns a necessary and sufficient condition that a generalizedquaternion square matrix is similar to a diagonal matrix.