# Limiting eigenvectors of outliers for Spiked Information-Plus-Noise type matrices

## TL;DR

This paper investigates the behavior of eigenvectors associated with outlier eigenvalues in spiked Information-Plus-Noise matrices, providing insights into their alignment with the underlying spikes and extending classical results.

## Contribution

It offers new theoretical results on eigenvector localization for outliers in spiked matrices, removing some technical assumptions from previous theorems.

## Key findings

- Eigenvectors of outliers project significantly onto the spike directions
- Extended classical results on eigenvalue separation without certain technical constraints
- Provides alternative proofs for eigenvalue support and separation phenomena

## Abstract

We consider an Information-Plus-Noise type matrix where the Information matrix is a spiked matrix. When some eigenvalues of the random matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the spikes. Note that, in an Appendix, we present alternative versions of the earlier results of Bai and Silverstein about the lack of eigenvalues outside the support of the deterministic equivalent measure and of Capitaine about the exact separation phenomenon, where we remove some technical assumptions.