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arXiv · 2312.04537

Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices

Kelly Bickel·Georgia Corbett·Annie Glenning·Changkun Guan·Martin Vollmayr-Lee
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Abstract

This paper studies the level set Crouzeix conjecture, which is a weak version of Crouzeix's conjecture that applies to finite compressions of the shift. Amongst other results, this paper establishes the level set Crouzeix conjecture for several classes of $3\times3$, $4\times4$, and $5\times5$ matrices associated to compressions of the shift via a geometric analysis of their numerical ranges. This paper also establishes Crouzeix's conjecture for several classes of nilpotent matrices whose studies are motivated by related compressions of shifts.

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Kelly Bickel, Georgia Corbett, Annie Glenning, Changkun Guan, Martin Vollmayr-Lee. 2023-12-07. Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices. https://arxiv.org/abs/2312.04537

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