On the geometry of the set of symmetric matrices with repeated eigenvalues
Algebraic Geometry
2018-07-18 v2 Differential Geometry
Abstract
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart-Young-Mirsky-type theorem for the distance function from a generic matrix to points in . We exhibit connections of our study to Real Algebraic Geometry (computing the Euclidean Distance Degree of ) and Random Matrix Theory.
Keywords
Cite
@article{arxiv.1807.04530,
title = {On the geometry of the set of symmetric matrices with repeated eigenvalues},
author = {Paul Breiding and Khazhgali Kozhasov and Antonio Lerario},
journal= {arXiv preprint arXiv:1807.04530},
year = {2018}
}