Geršgorin discs revisited

Let k, r, t be positive integers with k⩽r⩽t. For such a given triple of integers, we prove that there is a t × t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Geršgorin discs of A. Some examples and related results are also provided.