Geodesic
On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems
The electronic journal of linear algebra, Tome 4 (1998), pp. 19-31.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let A 2 F n$\Theta n$ , B 2 F n$\Theta t$ , where F is an arbitrary field. In this paper, the possible characteristic polynomials of [ A B ], when some of its columns are prescribed and the other columns vary, are described. The characteristic polynomial of [ A B ] is defined as the largest determinantal divisor (or the product of the invariant factors) of [ xI n $\Gamma A \Gamma B$ ]. This result generalizes a previous theorem by H. Wimmer which studies the same problem when t = 0. As a consequence, it is extended to arbitrary fields a result, already proved for infinite fields, that describes all the possible characteristic polynomials of a square matrix when an arbitrary submatrix is fixed and the other entries vary. Finally, applications to the stabilization and observability of linear systems by state feedback are studied.
Classification : 15A18, 93B60 
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     author = {Furtado, Susana and Silva, Fernando C.},
     title = {On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems},
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Furtado, Susana; Silva, Fernando C. On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems. The electronic journal of linear algebra, Tome 4 (1998), pp. 19-31. http://geodesic.mathdoc.fr/item/ELA_1998__4__a3/