Localization of dominant eigenpairs and planted communities by means of Frobenius inner products
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix . The result exploits the Frobenius inner product between and a given rank-one landmark matrix . Different choices for may be used, depending on the problem under investigation. In particular, we show that the choice where is the all-ones matrix allows to estimate the signature of the leading eigenvector of , generalizing previous results on Perron-Frobenius properties of matrices with...