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On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\). (English) Zbl 1019.15002

The authors study the solutions of the complex matrix equations \(X-AXB=C\) (for \(A=B^*\) this is the Stein equation) and \(X-A\bar{X}B=C\). They obtain an explicit solution of the former by the method of characteristic polynomials and of the latter by the method of real representations of a complex matrix.

MSC:

15A24 Matrix equations and identities
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References:

[1] Barnett, S.; Storey, C., Matrix Methods in Stability Theory (1970), Nelson: Nelson London · Zbl 0243.93017
[2] Barnett, S., Matrices in Control Theory with Applications to Linear Programming (1971), Van Nostrand Reinhold: Van Nostrand Reinhold New York · Zbl 0245.93002
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