Solvability and uniqueness criteria for generalized Sylvester-type equations
De Teran F., Iannazzo B., Poloni F., Robol L.
Functional Analysis (math.FA) Geometry and Topology FOS: Mathematics Mathematics - Functional Analysis Sylvester equation Mathematics - Rings and Algebras Mathematics - Numerical Analysis 15A24 Algebra and Number Theory Numerical Analysis 15A22 Eigenvalues Matrix pencil 65F15 Numerical Analysis (math.NA) Matrix equation Rings and Algebras (math.RA) Discrete Mathematics and Combinatorics
We provide necessary and sufficient conditions for the generalized (star operator)-Sylvester matrix equation, AXB+CX(star operator)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 operator)-Sylvester equations.
Source: Linear algebra and its applications 542 (2018): 501–521. doi:10.1016/j.laa.2017.07.010
Publisher: North Holland [etc.], [New York], Stati Uniti d'America
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@article{oai:it.cnr:prodotti:376258,
title = {Solvability and uniqueness criteria for generalized Sylvester-type equations},
author = {De Teran F. and Iannazzo B. and Poloni F. and Robol L.},
publisher = {North Holland [etc.], [New York], Stati Uniti d'America},
doi = {10.1016/j.laa.2017.07.010 and 10.48550/arxiv.1608.01183},
journal = {Linear algebra and its applications},
volume = {542},
pages = {501–521},
year = {2018}
}
0000-0002-6545-1748ISTI Repository
DOI
10.1016/j.laa.2017.07.010
10.48550/arxiv.1608.01183
arXiv.org e-Print Archive
Linear Algebra and its Applications
www.sciencedirect.com