Applied Mathematics and Mechanics (English Edition) ›› 1995, Vol. 16 ›› Issue (12): 1133-1141.

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THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

Chen Yuming1, Xiao Heng2   

  1. 1. Department of Applied Mathematics, Hunan University, Changsha 410012, P.R.China;
    2. Department of Mathematics, Peking University, Beijing 100871, P.R.China
  • Received:1995-02-28 Online:1995-12-18 Published:1995-12-18
  • Supported by:
    Project Supported by the National Natural Science Foundation of China

Abstract: Almost all of the existing results on the explicit solutions of the matrix equation AX-XB=C are obtained under the condition that A and B have no eigenvalues incommon For both symmetric or skewsymmetric matrices A and B. we shall give outthe explicit general solutions of this equation by using the notions of eigenprojectionsThe results we obtained are applicable not only to any cases of eigenvalues regardlessof their multiplicities but also to the discussion of the general case of this equation.

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