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The convex algebraic geometry of higher-rank numerical ranges
Jonathan Nino-Cortes, Cynthia Vinzant·October 29, 2024·DOI: 10.1016/j.jsc.2025.102457
Computer ScienceMathematics
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Abstract
The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. We will discuss some of the real algebraic and convex geometry of these sets, including a generalization of Kippenhahn's theorem, and describe an algorithm to explicitly calculate the higher-rank numerical range of a given matrix.