The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices

Pierre Bousseyroux; Marc Potters

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arXiv · 2601.10427

The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices

Pierre Bousseyroux·Marc Potters

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Abstract

We study finite-rank normal deformations of rotationally invariant non-Hermitian random matrices. Extending the classical Baik-Ben Arous-P\'ech\'e (BBP) framework, we characterize the emergence and fluctuations of outlier eigenvalues in models of the form $\mathbf{A} + \mathbf{T}$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix and $\mathbf{T}$ is a finite-rank normal perturbation. We also describe the corresponding eigenvector behavior. Our results provide a unified framework encompassing both Hermitian and non-Hermitian settings, thereby generalizing several known cases.

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Pierre Bousseyroux, Marc Potters. 2026-01-15. The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices. https://arxiv.org/abs/2601.10427

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