# Restricted numerical range

## Definition

Restricted numerical range of an $d \times d$ matrix $A$ is defined as: $W_\mathrm{R}(A) = \left\{ \mathrm{Tr}A\rho, \; \rho \in \Omega_\mathrm{R} \subset \Omega \right\}$. The symbol $\Omega_\mathrm{R}$ denotes any arbitrary subset of set $\Omega$ of all normalized density matrices of dimension $d$.