Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A short proof of the fact that the matrix trace is the expectation of
  the numerical values   Using the fact that the normalised matrix trace is the unique linear
functional $f$ on the algebra of $n\times n$ matrices which satisfies $f(I)=1$
and $f(AB)=f(BA)$ for all $n\times n$ matrices $A$ and $B$, we derive a
well-known formula expressing the normalised trace of a complex matrix $A$ as
the expectation of the numerical values of $A$; that is the function $\langle
Ax,x\rangle$, where $x$ ranges the unit sphere of $\mathbb{C}^n$.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an