  A matrix is well separated if all its Gershgorin circles are away from the
unit circle and they are separated from each other. In this article, the region
of relative errors in the eigenvalues is obtained as a quadratic oval for non
diagonal perturbation of well seperated matrices. Thus giving a computable
relative error bound in terms of Gershgorin circle parameters. When the
separation is $O(n)$ and the matrix is positive definite, an interlacing
theorem for the eigenvalues under perturbation is presented. Further when the
separation is $O(n^2 )$, condition number of the eigenvector matrix is upper
bounded to obtain the region of perturbed eigenvalue. Numerical results show
the relation between diagonal entries and the magnitude of the eigenvector
entries even when the matrix is not so well separated. We exploit this trend in
estimating the Perron vector using power method.
