On the Uniqueness of Functions that Maximize the Crouzeix Ratio

Kenan Li

Let $A$ be an $n$ by $n$ matrix with numerical range $W(A):=\{q^{\ast }Aq:q\in {\mathbb{C}}^n,\Vert q{\Vert }_2=1\}$. We are interested in functions $\hat{f}$ that maximize $\| f(A)…