Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: About the matrix function X->AX+XA   Let K be an infinite field such that its characteristic is not 2. We show
that, for every $A\in\mathcal{M}_n(K)$ such that $\mathrm{rank}(A)\geq n/2$,
there exists $B\in\mathcal{M}_n(K)$ such that $B$ is similar to $A$ and $A+B$
is invertible. Let $K$ be a subfield of $\mathbb{R}$. We show that, if $n$ is
even, then for every $X\in\mathcal{M}_n(K)$, $\det(AX+XA)\geq 0$ if and only if
either $\mathrm{rank}(A)<n/2$ or there exists $\alpha\in K,\alpha\leq 0$, such
that $A^2=\alpha I_n$.

34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys