Solvability and uniqueness criteria for generalized Sylvester-type equations

Fernando De Terán; Bruno Iannazzo; Federico Poloni; Leonardo Robol

doi:10.1016/j.laa.2017.10.018

Solvability and uniqueness criteria for generalized Sylvester-type equations

Rings and Algebras 2021-03-17 v3 Functional Analysis Numerical Analysis

Authors: Fernando De Terán , Bruno Iannazzo , Federico Poloni , Leonardo Robol

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Abstract

We provide necessary and sufficient conditions for the generalized $\star$ -Sylvester matrix equation, $AXB + CX^\star D = E$ , to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices $A, B, C, D$ (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the existence and uniqueness of solution for generalized Sylvester and $\star$ -Sylvester equations.

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@article{arxiv.1608.01183,
  title  = {Solvability and uniqueness criteria for generalized Sylvester-type equations},
  author = {Fernando De Terán and Bruno Iannazzo and Federico Poloni and Leonardo Robol},
  journal= {arXiv preprint arXiv:1608.01183},
  year   = {2021}
}

Comments

This new version corrects some inaccuracies in corollaries 7 and 9

Solvability and uniqueness criteria for generalized Sylvester-type equations

Abstract

Cite

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