Algebra
Some matrix completion problems
Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 673-676.

Let F be a field and let n,p1,p2,p3 be positive integers such that n=p1+p2+p3. Let

A=[A1,1A1,2A1,3A2,1A2,2A2,3A3,1A3,2A3,3]Fn×n,
where the blocks Ai,j are of type pi×pj,i,j{1,2,3}, and the blocks in the positions (i,i) are square. We describe the characteristic polynomial of A, when:

(i) A1,1, A1,2 and A3,3 are fixed and the other blocks vary;

(ii) A1,1, A1,2 and A2,3 are fixed and the remaining blocks vary.

Soit F un corps et soient n,p1,p2,p3 des entiers positifs tels que n=p1+p2+p3. Soit

A=[A1,1A1,2A1,3A2,1A2,2A2,3A3,1A3,2A3,3]Fn×n,
où les blocs Ai,j sont de type pi×pj,i,j{1,2,3}. Nous étudions le polynôme caractéristique de la matrice A, quand :

(i) A1,1,A1,2 et A3,3 sont connus et les autres blocs varient ;

(ii) A1,1,A1,2 et A2,3 sont connus et les autres blocs varient.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.04.016
Cravo, Glória 1

1 Departamento de Matemática e Engenharias, Universidade da Madeira, 9000-390 Funchal, Madeira, Portugal
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Cravo, Glória. Some matrix completion problems. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 673-676. doi : 10.1016/j.crma.2007.04.016. http://www.numdam.org/articles/10.1016/j.crma.2007.04.016/

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