Solution theory for systems of bilinear equations
Charles R. Johnson, Helena Šmigoc, Dian Yang · Linear and Multilinear Algebra · 2013
Bilinear systems of equations are defined, motivated and analysed 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.