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numerical-range:generalizations:restricted-numerical-range

# Restricted numerical range

## Definition

Restricted numerical range of an $N \times N$ 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 and arbitrary subset of set $\Omega$ of all normalized density matrices of size $N$.