Eigenvalue condition numbers and a formula of Burke, Lewis and Overton
Michael Karow · Electronic Journal of Linear Algebra · 2006
In a paper by Burke, Lewis and Overton, a first order expansion has been given forthe minimum singular value of A−zI, z ∈ C, about a nonderogatory eigenvalue λ of A ∈ Cn×n. Thisnote 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.