CONICET | Buscador de Institutos y Recursos Humanos

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 firstKoszul map) and prove that these new theorems serve to solve overdeterminedsparse systems and to count the expected number of solutions.