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The convex algebraic geometry of higher-rank numerical ranges

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arxiv 2410.21625 v1 pith:BWLNG4AR submitted 2024-10-29 math.FA math.AG

Jonathan Nino-Cortes , Cynthia Vinzant This is my paper · ORCID
classification math.FAmath.AG
keywords numericalconvexhigher-rankrangealgebraicgeometrymatrixalgorithm
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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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    math.OC 2025-07 conditional novelty 4.0 of 10

    After preconditioning the defining linear map, global minimization of the dual log-partition function certifies moment body membership, and L-BFGS handles dense n=m=1000 instances in seconds.

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