Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural Isomorphism from a Linear Map's Image to Complement of Nullspace   There is a natural isomorphism from image to complement of nullspace, for a
bounded linear map from a real Banach space onto a closed subspace of a real
Hilbert space. This generalizes Riesz representation (self-duality of Hilbert
space). The isomorphism helps solve the pressure equation of fluid dynamics.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga