Resumen de A new proof of Fillmore’s theorem for integer matrices

Rocio Velasco Olalla

• Fillmore’s theorem is a matrix completion problem that states that if A is a nonscalar matrix over a field F and ϒ1,..., ϒ n ∈ F so that ϒ 1 +...+ ϒ n = tr(A) then there is a matrix similar to A with diagonal (ϒ1,..., ϒn). Borobia [1] extended Fillmore’s Theorem to the matrices over the ring of integers and Soto, Julio and Collao [3] studied it with the nonnegativity hypothesis. In this paper we prove the same result by modifying the initial proof of Fillmore, a subsequent new algorithm is proposed and some new information about the final matrix will be given.