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The convex algebraic geometry of higher-rank numerical ranges

Functional Analysis 2024-10-30 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.2410.21625,
  title  = {The convex algebraic geometry of higher-rank numerical ranges},
  author = {Jonathan Nino-Cortes and Cynthia Vinzant},
  journal= {arXiv preprint arXiv:2410.21625},
  year   = {2024}
}

Comments

26 pages, 8 figures