Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.
Belinschi, Hari Bercovici, Mireille Capitaine, and Maxime F´ evrier
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The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices
Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.