四元数矩阵的广义逆  

The Generalized Inverse of Quaternion Matrices

作　　者：刘波[1] 张爱萍[2] 

机构地区：[1]桂林电子工业学院计算科学与数学系,广西桂林541004 [2]合肥工业大学理学院,安徽合肥230009

出　　处：《桂林电子工业学院学报》2004年第5期68-71,共4页Journal of Guilin Institute of Electronic Technology

摘　　要：四元数和四元数矩阵在量子物理学、计算机图形学等许多领域得到了应用,但由于四元数的乘法不满足交换律,阻碍了对四元数矩阵的研究,尤其是关于四元数矩阵广义逆的讨论还不多。将复数域上矩阵的广义逆的理论推广到四元数体上,得到了在四元数体上m×n阶矩阵的减号逆、最小二乘广义逆、极小范数广义逆和加号逆的通式,并且讨论了这些广义逆具有的一些性质。应用这些结论可以进一步解决四元数体上矩阵方程的求解问题。Quaternion and quaternion matrices have been applied in many fields, such as in quantum physics and computer graphics. However, since the multiplication of quaternion is non-commutative, there exist the main obstacles in the study of quaternion matrices. Furthermore, the study on the generalized inverse of quaternion matrices is far from enough. This paper extends the theory of generalized inverse of matrices over the complex number field to the quaternion skew field. As a result, we can not only get the construction of {1}-,{1,3}-,{1,4}-and{1,2,3,4}-inverse over the quaternion, but also get some properties for these generalized inverses. These conclusions are applied to the study of quaternion matrices equation.

关 键 词：四元数 四元数矩阵 广义逆 

分 类 号：O151.21[理学—数学]