The common invariant subspace problem: an approach via Gröbner bases

@article{Arapura2004TheCI,
title={The common invariant subspace problem: an approach via Gr{\"o}bner bases},
author={D. Arapura and C. Peterson},
journal={Linear Algebra and its Applications},
year={2004},
volume={384},
pages={1-7}
}

Let A be an n × n matrix. It is a relatively simple process to construct a homogeneous ideal (generated by quadrics) whose associated projective variety parametrizes the one-dimensional invariant subspaces of A. Given a finite collection of n × n matrices, one can similarly construct a homogeneous ideal (again generated by quadrics) whose associated projective variety parametrizes the one-dimensional subspaces which are invariant subspaces for every member of the collection. Grobner basis… Expand