Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polarization Identities   We prove a generalization of the polarization identity of linear algebra
expressing the inner product of a complex inner product space in terms of the
norm, where the field of scalars is extended to an associative algebra equipped
with an involution, and polarization is viewed as an averaging operation over a
compact multiplicative subgroup of the scalars. Using this we prove a general
form of the Jordan-von Neumann theorem on characterizing inner product spaces
among normed linear spaces, when the scalars are taken in an associative
algebra.

7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an