Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On simultaneous diagonalization via congruence of real symmetric
  matrices   Deciding whether more than two real symmetric matrices can be simultaneously
diagonalizable via congruence has been a long
  standing problem. It is known as the SDC problem. The best results so far in
literature were only sufficient, which rely on the existence of a positive
semidefinite matrix pencil.
  In this paper, we prove necessary and sufficient conditions to characterize
the SDC problem and provide an iterative
  algorithm to simultaneously diagonalize all of them.

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc