Conditions for minimizing the norm sensitivity of characteristic roots

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 ?? denote a real root and ?? + j ?? a complex root. Conditions for minimizing the sensitivity norms based on ??, ??, ?? and |?? + j ??| are obtained. Since the conditions apply for all n and involve simple algebraic properties of the matrix, they may have useful applications.