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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09734 |
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Table of Contents:
- We show that the spectrum of the open-boundary limit of banded Toeplitz matrices is real whenever the associated symbol function is real-valued along a closed polar curve. Building on this result, we develop both analytical and numerical methods to symmetrise a class of banded non-Hermitian Toeplitz matrices whose asymptotic spectra are real. Finally, we provide a rigorous mathematical foundation for the generalised Brillouin zone, a concept widely used in non-Hermitian physics, by proving that it coincides with the polar curve on which the symbol function takes real values.