No abstract

No abstract

This paper refines the work on Geršgorin Discs in the article "Geometric Multiplicities and Geršgorin Discs", The American Mathematical Monthly, 120(2013), 452-455 by R. Marsli and F. Hall. Some consequences of this refinement and examples are provided.

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.

No abstract