The web resource on numerical range and numerical shadow

Hermitian matrices

In the case of Hermitian matrices the numerical shadow is a one dimensional distribution.

Diagonal matrices

Example 1

The matrix is $\mathrm{diag}(1, 2, 3, 4 ,5)$. The dashed lines mark the eigenvalues. The upped plot shows the derivative of the distribution.

Standard numerical shadow with respect to complex states. Numerical shadow with respect to real states.

Example 2

The matrix is $\mathrm{diag}(1, 2, 2, 4 ,5)$. The dashed lines mark the eigenvalues. The upped plot shows the derivative of the distribution.

Standard numerical shadow with respect to complex states. Numerical shadow with respect to real states.

Example 3

The matrix is $\mathrm{diag}(1, 2, 2, 2 ,5)$. The dashed lines mark the eigenvalues. The upped plot shows the derivative of the distribution.

Standard numerical shadow with respect to complex states. Numerical shadow with respect to real states.

Example 4

The matrix is $\mathrm{diag}(1, 1, 3, 4, 6)$. The dashed lines mark the eigenvalues. The upped plot shows the derivative of the distribution.

Standard numerical shadow with respect to complex states. Numerical shadow with respect to real states.