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arXiv · 2410.21625

The convex algebraic geometry of higher-rank numerical ranges

Jonathan Nino-Cortes·Cynthia Vinzant
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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.

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Jonathan Nino-Cortes, Cynthia Vinzant. 2024-10-29. The convex algebraic geometry of higher-rank numerical ranges. https://arxiv.org/abs/2410.21625

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