If, in addition to the above adjustments, each node is given weight equal to its row sum in the matrix-vector multiplication, the resulting eigenvector will be the one corresponding to the first ...

Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λ 0 of X0, so that the triple (X0,u0,λ 0) satisfies the equations Xu = λu, u0 * u=1. We ...

Boaz Nadler, Finite Sample Approximation Results for Principal Component Analysis: A Matrix Perturbation Approach, The Annals of Statistics, Vol. 36, No. 6, High Dimensional Inference and Random ...