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.

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

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title = {Some matrix completion problems},
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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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