Location of Ritz values in the numerical range of normal matrices

Abstract

Let ${\mu }_1$ be a complex number in the numerical range $W(A)$ of a normal matrix $A$. In the case when no eigenvalues of $A$ lie in the interior of $W(A)$, we identify the smallest convex region containing all possible complex numbers ${\mu }_2$ for which $\left[\begin{array}{cc}{\mu }_1& \ast \\ 0& {\mu }_2\end{array}\right]$ is a $2$-by-$2$ compression of $A$.

32 pages