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Positive semidefinite rank and nested spectrahedra. (English) Zbl 1395.14041
Summary: The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture for the description of this boundary. Our proof techniques are geometric in nature and rely on nesting spectrahedra between polytopes.

MSC:
14P10 Semialgebraic sets and related spaces
15B48 Positive matrices and their generalizations; cones of matrices
15A23 Factorization of matrices
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