Computing the leading eigenvector of a symmetric real matrix is a fundamental primitive of numerical linear algebra with numerous applications. We consider a natural online extension of the leading eigenvector problem: a sequence of matrices is presented and the goal is to predict for each matrix a unit vector, with the overall goal of competing with the leading eigenvector of the cumulative ma...

This paper gives double angle theorems that bound the change in an invariant subspace of an inde nite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a de nite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only r...

Double orthogonality in the set of eigenvectors of any symmetric graph matrix is exploited to propose a set of nodal centrality metrics, that is “ideal” in the sense of being complete, uncorrelated and mathematically precisely defined and computable. Moreover, we show that, for each node m, such a nodal eigenvector centrality metric reflects the impact of the removal of node m from the graph at...