Jiang, Tongsong; Wei, Musheng On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\). (English) Zbl 1019.15002 Linear Algebra Appl. 367, 225-233 (2003). 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. Reviewer: Vladimir P.Kostov (Nice) Cited in 53 Documents MSC: 15A24 Matrix equations and identities Keywords:matrix equation; Stein equation; method of characteristic polynomial; method of real representations of a complex matrix; explicit solution PDFBibTeX XMLCite \textit{T. Jiang} and \textit{M. Wei}, Linear Algebra Appl. 367, 225--233 (2003; Zbl 1019.15002) Full Text: DOI 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 [3] Jameson, A., Solution of the equation \(AX − XB =C\) by inversion of an \(M\)×\(M\) or ((N×N\) matrix, SIAM J. Appl. Math., 16, 1020-1023 (1968) · Zbl 0169.35202 [4] Lancaster, P.; Tismenetsky, M., The Theory of Matrices with Applications (1985), Academic Press: Academic Press New York · Zbl 0516.15018 [5] Ben-Israel, A.; Greville, T. N.E, Generalized Inverses: Theory and Applications (1974), Wiley: Wiley New York · Zbl 0305.15001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.