arXiv:2606.20432

Eigenvector Varieties

Sandra Di Rocco, Bernd Sturmfels, Svala Sverrisdóttir

math.AGmath.RAquant-phSubmitted Jun 18, 2026• Announced Jun 19, 2026• Revised Aug 18, 2026 (v2)

Abstract

Any linear space of square matrices has an associated eigenvector variety. Its points are eigenvectors of matrices from that linear space. We present a systematic study of eigenvector varieties, with focus on Lie algebras and Hamiltonians of quantum systems.

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