Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices
Autor: | Bickel, Kelly, Corbett, Georgia, Glenning, Annie, Guan, Changkun, Vollmayr-Lee, Martin |
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Rok vydání: | 2023 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 28 pages |
Databáze: | arXiv |
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