Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Further refinements of the Cauchy-Schwarz inequality for matrices   Let $A, B$ and $X$ be $n\times n$ matrices such that $A, B$ are positive
semidefinite. We present some refinements of the matrix Cauchy-Schwarz
inequality by using some integration techniques and various refinements of the
Hermite--Hadamard inequality. In particular, we establish the inequality
\begin{align*}
|||\,|A^{1\over2}XB^{1\over2}|^r|||^2&\leq|||\,|A^{t}XB^{1-s}|^r|||
\,\,\,|||\,|A^{1-t}XB^{s}|^r|||\\& \leq\max \{|||\,|AX|^r|||
\,\,\,|||\,|XB|^r|||,|||\,|AXB|^r||| \,\,\,|||\,|X|^r|||\}, \end{align*} where
$s,t\in[0,1]$ and $r\geq0$.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat