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 n
²
derivatives with respect to the elements of the matrix. Let λ denote a real root and
\sigma + j\omega
a complex root. Conditions for minimizing the sensitivity norms based on
\lambda, \sigma, \omega,
and
|\sigma + j\omega|
are obtained. Since the conditions apply for all
n
and involve simple algebraic properties of the matrix, they may have useful applications.