If A is an nxn complex matrix and λ is an eigenvalue of A with geometric multiplicity k, then λ is in at least k of the Geršgorin discs Di of A. Let k, r, t be positive integers with k ≤ r ≤ t. Then there is a txt 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.

If A is an nxn complex matrix and λ is an eigenvalue of A with geometric multiplicity k, then λ is in at least k of the Geršgorin discs Di of A. Let k, r, t be positive integers with k ≤ r ≤ t. Then there is a txt 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.