Solution Theory for Systems of Bilinear Equations
Rings and Algebras
2013-03-21 v1
Abstract
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from elementary operations. This idea is used to identify bilinear systems that are solvable for all right hand sides and to understand solvability when the number of equations is large or small.
Cite
@article{arxiv.1303.4988,
title = {Solution Theory for Systems of Bilinear Equations},
author = {Charles R. Johnson and Helena Šmigoc and Dian Yang},
journal= {arXiv preprint arXiv:1303.4988},
year = {2013}
}