Uniqueness of solution of systems of generalized Sylvester and conjugate-Sylvester equations
Rings and Algebras
2025-03-18 v1
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.
Keywords
Cite
@article{arxiv.2503.12433,
title = {Uniqueness of solution of systems of generalized Sylvester and conjugate-Sylvester equations},
author = {Fernando De Terán and Bruno Iannazzo},
journal= {arXiv preprint arXiv:2503.12433},
year = {2025}
}