Solving a sparse systems using linear algebra

2012/11/15 by César Massri, Massri, César
Computer Science · Mathematics · #13P15 #14M25 #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1211.3715

openalex publication_date 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Some Formulae in Elimination

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