Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some inequalities of matrix power and Karcher means for positive linear
  maps   In this paper, we generalize some matrix inequalities involving matrix power
and Karcher means of positive definite matrices. Among other inequalities, it
is shown that if ${\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive
definite matrices such that $0<m\leq A_{i}\leq M\, (i=1,\cdots,n)$ for some
scalars $m< M$ and $\omega=(w_{1},\cdots,w_{n})$ is a weight vector with
$w_{i}\geq0$ and $\sum_{i=1}^{n}w_{i}=1$, then \begin{align*}
\Phi^{p}\Big(\sum_{i=1}^{n}w_{i}A_{i}\Big)\leq \alpha^{p}\Phi^{p}(P_{t}(\omega;
{\mathbb A})) \end{align*} and \begin{align*}
\Phi^{p}\Big(\sum_{i=1}^{n}w_{i}A_{i}\Big)\leq
\alpha^{p}\Phi^{p}(\Lambda(\omega; {\mathbb A})), \end{align*} where $p>0$,
$\alpha=\max\Big\{\frac{(M+m)^{2}}{4Mm},
\frac{(M+m)^{2}}{4^{\frac{2}{p}}Mm}\Big\}$, $\Phi$ is a positive unital linear
map and $t\in [-1, 1]\backslash \{0\}$.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org