Applied Mathematics and Mechanics

, Volume 16, Issue 12, pp 1133–1141 | Cite as

The explicit solution of the matrix equation AX−XB=C

  • Chen Yuming
  • Xiao Heng
Article

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 in common. For both symmetric or skewsymmetric matrices A and B, we shall give out the explicit general solutions of this equation by using the notions of eigenprojections. The results we obtained are applicable not only to any cases of eigenvalues regardless of their multiplicities, but also to the discussion of the general case of this equation.

Key words

matrix equation explicit solution eigenprojection matrix square-product 

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Copyright information

© SU Shanghai, China 1995

Authors and Affiliations

  • Chen Yuming
    • 1
  • Xiao Heng
    • 2
  1. 1.Department of Applied MathematicsHuman UniversityChangshaP. R. China
  2. 2.Department of MathematicsPeking UniversityBeijingP. R. China

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