Date Thesis Awarded
5-2011
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Charles R. Johnson
Committee Members
John Delos
C. Ryan Vinroot
Abstract
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 $\{A_i\}_{i=1}^m$.
Recommended Citation
Yang, Dian, "Solution Theory for Systems of Bilinear Equations" (2011). Undergraduate Honors Theses. William & Mary. Paper 415.
https://scholarworks.wm.edu/honorstheses/415
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Comments
Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.