Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free Semidefinite Representation of Matrix Power Functions   Consider the matrix power function X^p defined over the cone of positive
definite matrices S^{n}_{++}. It is known that X^p is convex over S^{n}_{++} if
p is in [-1,0] or [1,2] and X^p is concave over S^{n}_{++} if p is in [0,1]. We
show that the hypograph of X^p admits a free semidefinite representation if p
in [0,1] is rational, and the epigraph of X^p admits a free semidefinite
representation if p in [-1,0] or [1,2] is rational.

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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg