Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Matrix Inequality and Semidefinite Representation   Consider a convex set S defined by a matrix inequality of polynomials or
rational functions over a domain. The set S is called semidefinite programming
(SDP) representable or just semidefinite representable if it equals the
projection of a higher dimensional set which is defined by a linear matrix
inequality (LMI). This paper studies sufficient conditions guaranteeing
semidefinite representability of S. We prove that S is semidefinite
representable in the following cases: (i) the domain is the whole space and the
matrix polynomial is matrix sos-concave; (ii) the domain is compact convex and
the matrix polynomial is strictly matrix concave; (iii) the rational matrix
function is q-module matrix concave on the domain. Explicit constructions of
SDP representations are given. Some examples are illustrated.

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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph