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 n2 derivatives with respect to the elements of the matrix. Let λ denote a real root and σ + j σ a complex root. Conditions for minimizing the sensitivity norms based on λ, σ, ω and |σ+ j ω| are obtained. Since the conditions apply for all n and involve simple algebraic properties of the matrix, they may have useful applications.