Conditions for minimizing the norm sensitivity of characteristic roots

The sensitivity, of a characteristic root of annbynreal matrix is measured by the Euclidean norm of the root's n2derivatives with respect to the elements of the matrix. Let λ denote a real root andσ + j complex root. Conditions for minimizing the sensitivity norms based onλ, σ, ω,and|σ + jω|are obtained. Since the conditions apply for allnand involve simple algebraic properties of the matrix, they may have useful applications.