Preprint in the OpenAI Math release
A direct proof of the complete Crouzeix inequality
OpenAI
Abstract
We give a direct proof of the sharp constant-two numerical-range inequality for matrix-valued polynomials in all finite base and coefficient dimensions. This resolves the complete Crouzeix conjecture in its matrix formulation, including matrices whose numerical ranges are points or line segments.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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