Eigenvalue condition numbers and a formula of Burke, Lewis and Overton

Abstract

In a paper by Burke, Lewis and Overton, a first order expansion has been given for
the minimum singular value of A−zI, z ∈ C, about a nonderogatory eigenvalue λ of A ∈ C^n×n. This
note investigates the relationship of the expansion with the Jordan canonical form of A. Furthermore,
formulas for the condition number of eigenvalues are derived from the expansion.