Consider a cluster of m eigenvalues, counting multiplicities.
Similar notation is used for and .
We instead compute an estimate of as the reciprocal value of an estimate of , where Z u is the matrix representation of the generalized Sylvester operator. It is possible to estimate by solving generalized Sylvester equations in triangular form. The one norm estimate makes the condition estimation uniform with the nonsymmetric eigenvalue problem. The Frobenius norm estimate offers a low cost and equally reliable estimator. So it makes sense to compute an one norm estimate of .