Matrix eigenproblems are at the heart of polynomial system solving
Hans J. Stetter · ACM SIGSAM Bulletin · 1996
This note aims at illuminating the fact that matrix eigenproblems are not just some tool in the solution of polynomial systems of equations (cf.[7]) but t h a t --i n a sense to be shown--they represent the weakly nonlinear nucleus to which the original, strongly nonlinear task may be reduced.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.