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Invertible solutions to the operator equation $ TA-BT=C$


Author: David G. Luenberger
Journal: Proc. Amer. Math. Soc. 16 (1965), 1226-1229
MSC: Primary 47.10
DOI: https://doi.org/10.1090/S0002-9939-1965-0184088-0
MathSciNet review: 0184088
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References [Enhancements On Off] (What's this?)

  • [1] D. E. Rutherford, On the solution of the matrix equation $ AX + XB = C$, Nederl. Akad. Wetensch., Amsterdam Proc. Ser. A 35 (1932), 54-59.
  • [2] Marvin Rosenblum, On the operator equation 𝐵𝑋-𝑋𝐴=𝑄, Duke Math. J. 23 (1956), 263–269. MR 79235
  • [3] A. Lyapunov, Problème général de la stabilité du mouvement, Annals of Mathematics Studies No. 17, Princeton Univ. Press., Princeton, N. J., 1947.
  • [4] R. E. Kalman, Lyapunov functions for the problem of Lur′e in automatic control, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 201–205. MR 151696, https://doi.org/10.1073/pnas.49.2.201

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DOI: https://doi.org/10.1090/S0002-9939-1965-0184088-0
Article copyright: © Copyright 1965 American Mathematical Society