In the case of Hermitian matrices the numerical shadow is a one dimensional distribution.
The matrix is $\mathrm{diag}(0,6)$
Standard numerical shadow with respect to complex states. | Numerical shadow with respect to real states. |
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The matrix is $$\begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}.$$ The shadow resembles a physical shadow cast by the hollow sphere made of transparent material when illuminated by a light source at infinity.
Standard numerical shadow with respect to complex states. | Cross-section of the shadow along the real axis. |
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The matrix is $$\begin{pmatrix} 0&1\\ 0&1 \end{pmatrix}.$$ The shadow resembles physical shadow cast by the hollow sphere made of transparent material when illuminated by a light source at infinity, but with screen not perpendicular to the light rays.
Standard numerical shadow with respect to complex states. | Cross-section of the shadow along the real axis. |
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![]() | ![]() |