AlphaEvolve problems·alphaevolve:25

Crouzeix's Conjecture

record target F0 no formal statement

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Let $C$ be the smallest constant for which one has the bound $$ \\| p(A) \\|_{op} \\leq C \\sup_{z \\in W(A)} |p(z)| $$ for all $n \\times n$ square matrices $A$ and all polynomials $p$ with complex coefficients, where $\\| \\|_{op}$ is the operator norm and $$ W(A) \\coloneqq \\{ \\langle Ax, x \\rangle: \\|x\\| \\leq 1 \\}$$ is the numerical range of $A$. What is $C$? What polynomials $p$ attain

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AlphaEvolve

2025-11-05

unstated A2 directed V1 write-up F0 no formal statement

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F0 no formal statement None. No formal statement is attached to the result.

Computed from what the project declares and what the register holds, never from reading the mathematics. How fidelity is graded.

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