Reachability matrices and cyclic matrices

Augusto Ferrante, Harald K. Wimmer
2010 The Electronic Journal of Linear Algebra  
We study reachability matrices R(A, b) = [b, Ab, . . . , A n−1 b], where A is an n × n matrix over a field K and b is in K n . We characterize those matrices that are reachability matrices for some pair (A, b) . In the case of a cyclic matrix A and an n-vector of indeterminates x, we derive a factorization of the polynomial det R(A, x) .
doi:10.13001/1081-3810.1360 fatcat:xo2fkz3kgjewjaoixvm6brg42m