Ranks of the common solution to six quaternion matrix equations



A new expression is established for the common solution to six classical linear quaternion matrix equations A1X = C1, XB1 = C3, A2X = C2, XB2 = C4, A3XB3 = C5, A4XB4 = C6 which was investigated recently by Wang, Chang and Ning (Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195: 721–732 (2008)). Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper.


system of matrix equations quaternion matrix minimal rank maximal rank linear matrix expression generalized inverse 

2000 MR Subject Classification

15A03 15A09 15A24 15A33 

Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina

Personalised recommendations