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.
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Communicated by Chien Weizang
To the memory of Prof. Guo Zhongheng
Project Supported by the National Natural Science Foundation of China
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Yuming, C., Heng, X. The explicit solution of the matrix equation AX−XB=C. Appl Math Mech 16, 1133–1141 (1995). https://doi.org/10.1007/BF02466983
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DOI: https://doi.org/10.1007/BF02466983