The web resource on numerical range and numerical shadow

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Example of a product numerical shadow restricted to real states of matrix $$\begin{pmatrix} 1&1&1&1\\ 0&i&1&1\\ 0&0&-1&1\\ 0&0&0&-i \end{pmatrix}$$ is forming an image of $\mathbb{R}P^1\times\mathbb{R}P^1$.