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)].
REACHABILITY MATRICES AND CYCLIC MATRICES
FERRANTE, AUGUSTO;
2010
Abstract
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)].File in questo prodotto:
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