四元数矩阵微分及其在精确分布上的应用

讨论了四元数矩阵的外微分形式，得出四元数矩阵变换下Ｊａｃｏｂｉ行列式的一些结果，利用这些结果，简化了四元数Ｗｉｓｈａｒｔ分布的推导，并且在求得四元数Ｓｔｉｅｆｅｌ流形体积的基础上，进一步导出其特征根分布

Exterior Differential Forms on Quaternion Matrices and Its Application

It is frequent that quaternion matrix transformations are used in deriving many important quaternion distributins.In these cases,several exterior differential forms on quaternion matrices given in this paper are crucial in the derivation of many density functions.We also give the volume of the Stiefel manifold on the quaternion.By using these results,we directly derive the density function of Wishart matrix,which dramatically simplifies the existing derivation of Wishart distribution.Finally,we acquire the density functin of latent roots of quaternion Wishart matrix.