We present necessary and sufficient conditions for the existence of a unique solution of the matrix equation $AXB+CX^star D=E$, where $A,B,C,D,E$ are square matrices of the same size with real or complex entries, and where $star$ stands for both the transpose or the conjugate transpose. This generalizes several previous uniqueness results for specific equations such as the $star$-Sylvester or the $star$-Stein equation.

Uniqueness of solution of a generalized $star$-Sylvester matrix equation

IANNAZZO, Bruno
2016

Abstract

We present necessary and sufficient conditions for the existence of a unique solution of the matrix equation $AXB+CX^star D=E$, where $A,B,C,D,E$ are square matrices of the same size with real or complex entries, and where $star$ stands for both the transpose or the conjugate transpose. This generalizes several previous uniqueness results for specific equations such as the $star$-Sylvester or the $star$-Stein equation.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1350847
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