ELLIPTIC NUMERICAL RANGES OF BORDERED MATRICES
Mao-Ting Chien, Kuo‐Chih Hung · Taiwanese Journal of Mathematics · 2012
Let $A \in M_n(C)$. The numerical range of $A$ is defined as $W(A) = \{x^*Ax: x \in C^n, |x|=1 \}$. We give a necessary and sufficient condition for $W(A)$ to be an elliptic disk. The criterion is applied to prove the elliptic numerical ranges of certain bordered matrices.