Details:
Title  The common invariant subspace problem: an approach via Gröbner bases  Author(s)  Donu Arapura, Chris Peterson  Type  Article in Journal  Abstract  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 onedimensional 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 onedimensional subspaces which are invariant subspaces for every member of the collection. Gröbner basis techniques then provide a finite, rational algorithm to determine how many points are on this variety. In other words, a finite, rational algorithm is given to determine both the existence and quantity of common onedimensional invariant subspaces to a set of matrices. This is then extended, for each d, to an algorithm to determine both the existence and quantity of common ddimensional invariant subspaces to a set of matrices.  Keywords  Eigenvector, Invariant subspace, Grassmann variety, Grobner basis, Algorithm  ISSN  00243795 
URL 
http://www.sciencedirect.com/science/article/pii/S0024379503008589 
Language  English  Journal  Linear Algebra and its Applications  Volume  384  Pages  1  7  Year  2004  Edition  0  Translation 
No  Refereed 
No 
