Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 743-752.

• Articles • Previous Articles     Next Articles

The Generalized (Anti)reflexive Solutions to a System of Quaternion Matrix Equations

 ZHANG Qin1, WANG Qing-Wen1*, CHANG Hai-Xia2   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444|2. Shanghai Finance University, Shanghai 201209
  • Received:2008-10-08 Revised:2009-12-30 Online:2010-05-25 Published:2010-05-25
  • Contact: wqw858@yahoo.com.cn E-mail:wqw858@yahoo.com.cn
  • Supported by:

    国家自然科学基金(60672160)、上海市教委创新基金(09YZ13)和上海市教委重点学科建设项目(J50101)资助

Abstract:

We give necessary and sufficient conditions for the existence of the general solution to the system of quaternion matrix equations  X1B1=C1, X2B2=C2, A1X1B3+A2X2B4=Cb . When the solvability conditions are met, we present an expression of the general solution to this system. Using the results on this system, we investigate necessary and sufficient conditions for the existence of generalized reflexive and generalized antireflexive solutions to the system of quaternion matrix equations XBa=Ca, AbXBb=Cb . We present expressions of the generalized reflexive and generalized antireflexive solutions to the system mentioned above when the solvability condtions are satisfied.

Key words: Quaternion, Quaternion matrix, Moore-Penrose inverse, System of matrix equations, Generalized reflexive matrix

CLC Number: 

  • 15A24
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