Generic Features in the Spectral Decomposition of Correlation Matrices
Mathematical Physics
2021-08-25 v1 math.MP
Abstract
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the alignment of the corresponding eigenvector. We explain how and to which extent, a distinctly large eigenvalue and an approximately diagonal eigenvector generically occur for specific correlation matrices independently of the correlation matrix dimension.
Cite
@article{arxiv.2104.08966,
title = {Generic Features in the Spectral Decomposition of Correlation Matrices},
author = {Yuriy Stepanov and Hendrik Herrmann and Thomas Guhr},
journal= {arXiv preprint arXiv:2104.08966},
year = {2021}
}