摘要
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。
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.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
北大核心
1999年第3期12-16,共5页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
中山大学高等学术基金
关键词
四元数
外微分式
WISHART分布
矩阵
微分
quaternion
quaternion normal distribution
quaternion Wishart distribution
exterior differential form
