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arXiv · 2503.12433

Uniqueness of solution of systems of generalized Sylvester and conjugate-Sylvester equations

Fernando De Terán·Bruno Iannazzo
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Abstract

We provide a characterization for a periodic system of generalized Sylvester and conjugate-Sylvester equations, with at most one generalized conjugate-Sylvester equation, to have a unique solution when all coefficient matrices are square and all unknown matrices of the system have the same size. We also present a procedure to reduce an arbitrary system of generalized Sylvester and conjugate-Sylvester equations to periodic systems having at most one generalized conjugate-Sylvester equation. Therefore, the obtained characterization for the uniqueness of solution of periodic systems provides a characterization for general systems of generalized Sylvester and conjugate-Sylvester equations.

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Fernando De Terán, Bruno Iannazzo. 2025-03-16. Uniqueness of solution of systems of generalized Sylvester and conjugate-Sylvester equations. https://arxiv.org/abs/2503.12433

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