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numerical-range:generalizations:restricted-numerical-range:real-numerical-range

Real numerical range

Definition

Real numerical range $W^\mathbb{R}(A)$ of a matrix $A$ is a subset of the complex plane defined as $$W^\mathbb{R}(A)=\{z:z=\bra{\psi}A\ket{\psi},\ket{\psi}\in\mathbb{R}^N,\braket{\psi}{\psi}=1\}.$$