Matrix eigenproblems are at the heart of polynomial system solving

Abstract

This note aims at illuminating the fact that matrix eigenproblems are not just some tool in the solution of polynomial systems of equations (cf. While parts of the following exposition are meaningful also for other coefficient fields and/or for ideals of positive dimension, we will restrict our attention here to O-dimensional ideals in C [ x l , . . . , x s ] =: ~s. To keep the presentation expository, we have not fornmlated our rather straightforward observations in the form of theorems; but a reader with a moderate background in linear algebra and in commutative algebra will be able to supplement any missing formal arguments.