Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A general formula by $LDL^{T}$ decomposition for the type-I seesaw
  mechanism   By performing an approximate spectral decomposition to the inverse mass
matrix of the right-handed neutrinos $M^{-1}$, we obtain a basis-independent
formula for the type-I seesaw mechanism. Mathematically, it is based on the
generalized Cholesky (or $LDL^{T}$) decomposition of the symmetric matrix
$M^{-1} = L D L^{T}$, with a diagonal matrix $D$ and a lower unitriangular
matrix $L$. Since the diagonalization of $L$ can be inverted without solving
cubic equations, the formula will be useful to investigate general properties
of the mechanism, such as flavor symmetries, generalized $CP$ symmetries, and
fine-tunings.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin