Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: About the logarithm function over the matrices   We prove the following results: let x,y be (n,n) complex matrices such that
x,y,xy have no eigenvalue in ]-infinity,0] and log(xy)=log(x)+log(y). If n=2,
or if n>2 and x,y are simultaneously triangularizable, then x,y commute. In
both cases we reduce the problem to a result in complex analysis.

10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin