ELA, Volume 15, pp. 143-153, May 2006, abstract.

Eigenvalue Condition Numbers and a Formula of Burke, 
Lewis and Overton

Michael Karow

In a paper by Burke, Lewis and Overton, a first order
expansion has been given for the minimum singular value
of A-zI (z a complex number) about a nonderogatory
eigenvalue \lambda of an n x n complex matrix A. 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.