Matrix Completion Problems

Throughout the last decades, several results have been published in the area of the so-called Matrix Completion Problems. In this paper, we survey several results in this field. In particular, we describe the possible eigenvalues, the characteristic polynomial, the invariant polynomials, or the number of nontrivial invariant polynomials of a square matrix, over a field, when some of its entries are prescribed and the others vary. Finally, we present our contribution, generalizing some of the previous cases, to an n×n matrix partitioned into k×k blocks, with entries in a field, when some of its blocks are prescribed and the others vary.