The numerical range of a matrix $latex A\in\mathbb{C}^{n\times n}$, also known as the field of values, is the set of complex numbers $latex W(A) = \biggl\{\, \displaystyle\frac{z^*Az}{z^*z}: 0\ne z\in\mathbb{C}^n \,\biggr\}. $ The set $LATEX W(A)$ is compact and convex (a nontrivial property proved by Toeplitz and Hausdorff), and it contains all the eigenvalues of $LATEX…