Determinantal and eigenvalue inequalities for matrices with numerical ranges in a sector

Chi-Kwong Li, Nung-Sing Sze

Let $A = \pmatrix A_{11} & A_{12} \cr A_{21} & A_{22}\cr\pmatrix \in M_n$, where $A_{11}\in M_m$ with $m\le n/2$, be such that the numerical range of $A$ lies in the set $\{e^{iφ…