数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1298-1306.

• 论文 • 上一篇    下一篇

四元数体上Hermite矩阵的最小化问题

  

  1. 1.五邑大学数学物理系 广东江门 529020|2.湖南大学数学与计量经济学院 长沙 410082
  • 收稿日期:2007-11-27 修回日期:2009-04-20 出版日期:2009-10-25 发布日期:2009-10-25
  • 基金资助:

    湖南省自然科学基金(09JJ6012)和湖南省教育厅科研项目(O1C162)资助

Minimization Problem for Hermitian Matrices over the Quaternion Field

  1. 1.Department of Mathematics and Physics, Wuyi |University, Guangdong Jiangmen |529020|2.College of Mathematics and Econometrics, Hunan University, Changsha 410082
  • Received:2007-11-27 Revised:2009-04-20 Online:2009-10-25 Published:2009-10-25
  • Supported by:

    湖南省自然科学基金(09JJ6012)和湖南省教育厅科研项目(O1C162)资助

摘要:

该文建立了四元数矩阵对的标准相关分解(CCD-Q). 借助CCD-Q, GSVD-Q 和有限维内积空间中的投影定理, 该文得到了基于四元数矩阵方程$AXB=C$的Hermite矩阵最小化问题解的表达式.

关键词: 四元数矩阵方程, 最小化问题, CCD-Q, GSVD-Q

Abstract:

In this paper, the canonical correlation decomposition of quaternion matrices (CCD-Q) is established. Based on the CCD-Q, GSVD-Q, and the projection theorem in the finite dimensional inner product space, the expression of
minimization problem for Hermitian matrices associated with the quaternion matrix equation AXB=C is derived.

Key words: Quaternion matrix equation, Minimization problem, CCD-Q, GSVD-Q

中图分类号: 

  • 65F05