A new proof of Fillmore’s theorem for integer matrices
Velasco Olalla, Rocio
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  extended Fillmore’s Theorem to the matrices over the ring of integers and Soto, Julio and Collao  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.