Hermitian matrices
In the case of Hermitian matrices the numerical shadow is a one dimensional distribution.
Diagonal matrices
Example 1
The matrix is $\mathrm{diag}(1, 2, 3, 4, 5, 6, 7, 8, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 2
The matrix is $\mathrm{diag}(1, 2, 2, 4, 5, 6, 7, 8, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 3
The matrix is $\mathrm{diag}(1, 2, 2, 2, 5, 6, 7, 8, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 4
The matrix is $\mathrm{diag}(1, 2, 2, 2, 2, 2, 2, 8, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 5
The matrix is $\mathrm{diag}(1, 2, 2, 2, 2, 2, 2, 2, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 6
The matrix is $\mathrm{diag}(1, 2, 2, 2, 2, 6, 6, 6, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 7
The matrix is $\mathrm{diag}(1, 2, 2, 2, 6, 6, 6, 8, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |
Example 8
The matrix is $\mathrm{diag}(1, 1, 1, 1, 9, 9, 9, 9, 9)$
Numerical shadow with respect to complex product states | Numerical shadow with respect to real product states |
 |  |
Numerical shadow with respect to complex entangled states | Numerical shadow with respect to real entangled states |
 |  |