Reachability matrices and cyclic matrices
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 95-102.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We study reachability matrices $R(A, b)$ = [b, Ab, . . . , A n - 1 b ], where A is an n $\times n$ 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 $R(A, x)$ .
Classification : 15A03, 15A15, 93B05
Mots-clés : reachability matrix, krylow matrix, cyclic matrix, nonderogatory matrix, companion matrix, Vandermonde matrix, hautus test 
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     author = {Ferrante, Augusto and Wimmer, Harald K.},
     title = {Reachability matrices and cyclic matrices},
     journal = {ELA. The Electronic Journal of Linear Algebra},
     pages = {95--102},
     publisher = {mathdoc},
     volume = {20},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a47/}
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Ferrante, Augusto; Wimmer, Harald K. Reachability matrices and cyclic matrices. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 95-102. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a47/