Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (2): 320-327.

• Articles • Previous Articles     Next Articles

Procrustes Problem of Hermitian Degree k R-symmetric Matrix and Its Approximation Problem

 JIA Zhi-Gang1,2, WEI Mu-Sheng3, ZHAO Mei-Xiang4   

  1. 1.School of |Mathematical Sciences, Xuzhou Normal University, Jiangsu Xuzhou 221116;
    2.Department of Mathematics, East China Normal University, Shanghai 200241;
    3.Department of Mathematics, Shanghai Normal University, Scientific Computing|Key Laboratory of Shanghai Universities, Shanghai 200234;
    4.Kewen Institute, Xuzhou Normal University, Jiangsu Xuzhou 221116
  • Received:2008-05-18 Revised:2010-01-12 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    国家自然科学基金(11001144)、江苏省高校自然科学基金(10KJD110005)和毫米波国家重点实验室开放课题(K201008)资助

Abstract:

The class of Hermitian degree k R-symmetric matrices is characterized. Necessary and sufficient conditions and explicit formulations 
 of   Hermitian degree k R-symmetric solutions of | AX-V|=min and AX=V are respectively derived, where X, V in Cnχm are known matrices. For given matrix Cnχn, the unique common Hermitian degree k R-symmetric solution of | AX-V| and | A-B| is obtained.

Key words: k-th unit matrix, Hermitian degree k R-symmetry, Procrustes problem, Approximation

CLC Number: 

  • 15A09
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