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We present necessary and sufficient conditions for the existence of a unique solution of the generalized star-Sylvester matrix equation AXB + (CXD)-D-star = E, where A, B, C, D, E are square matrices of the same size with real or complex entries, and where star stands for either the transpose or the conjugate transpose. This generalizes several previous uniqueness results for specific equations like the star-Sylvester or the star-Stein equations. (C) 2015 Elsevier Inc. All rights reserved.
linear matrix equation; matrix pencil; sylvester equation; star-sylvester equation; star-stein equation; t -sylvester equation; eigenvalues; algorithms; ax