Changkun Guan Changkun Guan

Changkun Guan

Ph.D. student in Operations Research at Georgia Tech's H. Milton Stewart School of Industrial and Systems Engineering (ISyE).

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Crouzeix’s Conjecture, Compressions of Shifts, and Classes of Nilpotent Matrices

Published in Concrete Operators, 2024

Kelly Bickel, Georgia Corbett, Annie Glenning, Changkun Guan, Martin Vollmayr-Lee. "Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices." Concrete Operators, 2024.

This paper studies the level set Crouzeix conjecture, a weak version of Crouzeix’s conjecture that applies to finite compressions of the shift. Among other results, it establishes the level set Crouzeix conjecture for several classes of 3×3, 4×4, and 5×5 matrices associated to compressions of the shift, via a geometric analysis of their numerical ranges.

Journal version (Concrete Operators, De Gruyter) · arXiv:2312.04537