A matrix completion problem over integral domains: the case with 2n-3 prescribed entries

Let Λ={λ1,…,λn}, n⩾2, be a given multiset of elements in an integral domain R and let P be a matrix of order n with at most 2n-3 prescribed entries that belong to R. Under the assumption that each row, each column and the diagonal of P have at least one unprescribed entry, we prove that P can be completed over R to obtain a matrix A with spectrum Λ. We describe an algorithm to construct A. This result is an extension to integral domains of a classical completion result by Herskowitz for fields.