Conditions for minimizing the norm sensitivity of characteristic roots

Abstract
The sensitivity, of a characteristic root of an n by n real matrix is measured by the Euclidean norm of the root's n 2 derivatives with respect to the elements of the matrix. Let denote a real root and sigma + jomega a complex root. Conditions for minimizing the sensitivity norms based on lambda, sigma, omega, and |sigma + jomega| are obtained. Since the conditions apply for all n and involve simple algebraic properties of the matrix, they may have useful applications.