BOUNDS FOR SINGULAR-VALUES BASED ON THE EIGENVECTORS

For a nondefective matrix A membership-sign C(nxn), the known inequalities \lambda-k\/chi less-than-or-equal-to sigma-k less-than-or-equal-to \lambda-k\chi express a bound on the possible ratio between the k th singular value sigma-k of A and its k th eigenvalue lambda-k, based only on the condition number chi of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.