Let A and \({\tilde{A}}\) be \(n\times n\) -matrices whose eigenvalues enumerated with their multiplicities are \(\lambda _k\) and \({\tilde{\lambda }}_j\) \((j,k=1,..., n)\) , respectively. In terms of the determinant of A and Frobenius norm of \({\tilde{A}}\) we derive a bound for the relative spectral variation \(\max _{j}\min _{k} |\frac{{\tilde{\lambda }}_j}{\lambda _k}- 1|\) of \({\tilde{A}}\) with respect to A, provided A is invertible. In addition, in terms of the Frobenius norm of \({\tilde{A}}\) , we obtain a new bound for the absolute spectral variation \(\max _{j}\min _{k} |{\tilde{\lambda }}_j-\lambda _k|\) . In appropriate situations our results are considerably sharper than the well-known bounds.
