Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometry of the set of symmetric matrices with repeated
  eigenvalues   We investigate some geometric properties of the real algebraic variety
$\Delta$ 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 $\Delta$. We exhibit connections of our study to Real
Algebraic Geometry (computing the Euclidean Distance Degree of $\Delta$) and
Random Matrix Theory.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph