数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1189-1198.doi: 10.1016/S0252-9602(10)60116-6

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ESTIMATES OF THE DOUBLE DETERMINANTS OF QUATERNION MATRICES

 冯良贵, 程薇   

  1. Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China
  • 收稿日期:2007-06-08 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    This research was supported in part by NCET (NCET06-9-23) and NUDT (JC08-02-03)

ESTIMATES OF THE DOUBLE DETERMINANTS OF QUATERNION MATRICES

 FENG Liang-Gui, CHENG Wei   

  1. Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China
  • Received:2007-06-08 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    This research was supported in part by NCET (NCET06-9-23) and NUDT (JC08-02-03)

摘要:

An estimate  of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.

关键词: Assortive pair, double determinant, inequality, quaternion matrix

Abstract:

An estimate  of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.

Key words: Assortive pair, double determinant, inequality, quaternion matrix

中图分类号: 

  • 15A23