Solving a sparse systems using linear algebra
Algebraic Geometry
2015-08-07 v2
Abstract
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector theorem to work with a canonical rectangular matrix (the first Koszul map) and prove that these new theorems serve to solve overdetermined sparse systems and to count the expected number of solutions.
Cite
@article{arxiv.1211.3715,
title = {Solving a sparse systems using linear algebra},
author = {César Massri},
journal= {arXiv preprint arXiv:1211.3715},
year = {2015}
}