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Criterion of the solvability of matrix equations of the Lyapunov type

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Abstract

By using the theory of generalized inverse operators, we establish a criterion of the solvability of the Lyapunov-type matrix equations AX - XB = D and X - AXB = D and investigate the structure of the set of their solutions.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. A. Boichuk

  2. Shevshenko National University, Kiev

    S. A. Krivosheya

Authors
  1. A. A. Boichuk
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  2. S. A. Krivosheya
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1021–1026, August, 1998.

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Boichuk, A.A., Krivosheya, S.A. Criterion of the solvability of matrix equations of the Lyapunov type. Ukr Math J 50, 1162–1169 (1998). https://doi.org/10.1007/BF02513089

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  • DOI: https://doi.org/10.1007/BF02513089

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