# Matrix perturbation and Eigenvector Bound

Recently I've been learning Matrix perturbation theory. Many theorems deal with perturbation bound in $$l_2$$ norm, or more generally, unitarily invariant norm, like F-norm or others(Like Davis-Kahan's Sin$$\Theta$$ theorem). Here is my question, is there a direct $$l_1$$ bound for the eigenvectors under the assumptions that the original matrix is perturbed in terms of $$l_1$$ norm? Note the result of $$l_2$$ norm shouldn't be used, since there's equivalence in these norms.

Appreciate any hint provided!