Date Thesis Awarded


Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)




Charles R. Johnson

Committee Members

John Delos

C. Ryan Vinroot


For $A_1,\ldots , A_m\in M_{p,q}(\mathbb{F})$ and $g\in\mathbb{F}^m$, any system of equations of the form $y^TA_ix=g_i$, $i=1,\ldots, m$, with $y$ varying over $\mathbb{F}^p$ and $x$ varying over $\mathbb{F}^q$ is called bilinear. A solution theory for complete systems ($m=pq$) is given in \cite{MR2567143}. In this paper we give a general solution theory for bilinear systems of equations. For this, we notice a relationship between bilinear systems and linear systems. In particular we prove that the problem of solving a bilinear system is equivalent to finding rank one points of an affine matrix function. And we study how in general the rank one completion problem can be solved. We also study systems with certain left hand side matrices $\{A_i\}_{i=1}^m$ such that a solution exist no matter what right hand side $g$ is. Criteria are given to distinguish such $\{A_i\}_{i=1}^m$.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.


Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

On-Campus Access Only