Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New proofs of the operator monotony of the square root and the inverse   Let $A,B\in B(H)$. We present among others a simple proof of the widely known
result stating that if $0\leq A\leq B$, then $\sqrt A\leq \sqrt B$. The same
idea is used to prove that if $0\leq A\leq B$ and $A$ is invertible, then $B$
too is invertible and $B^{-1}\leq A^{-1}$.

37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom