Eigenvalues of positive semi definite matrices generated using rand_herm are not random

Describe the issue I was trying to generate random positive semi-definite matrices using the function rand_herm but the eigenvalues clearly don’t seem to be random. For example, if I choose the dimension to be 3, then the eigenvalues are always like 3.something or 4.something or 5.something; if I choose the dimension to be 4, the eigenvalues are always like '4.somethingor5.somethingor6.something`, and similarly for other dimensions.

To Reproduce

import numpy as np
from numpy.linalg import eig

N = 4
for i in range(10):
    E = qutip.rand_herm(N, 0.35, None, True, None)
    w,v=eig(E)
    print('E-value:', w.real)

The terminal output is

E-value: [6.32043755 6.06791959 5.24578891 4.99327095]
E-value: [5.37493846 5.8003551  6.26253682 5.65685425]
E-value: [5.17596435 5.5020902  5.8116183  6.13774415]
E-value: [6.25884718 5.05486132 5.71761238 5.59609612]
E-value: [5.94609905 5.36760945 6.2943825  5.33641017]
E-value: [6.25296302 5.06074548 5.65685425 5.65685425]
E-value: [4.81999397 5.75787997 6.57166109 5.65685425]
E-value: [5.23867334 6.35633232 5.8283425  5.65685425]
E-value: [5.13755732 5.71669004 6.21844559 5.65685425]
E-value: [6.32817223 5.48538456 5.30187642 6.01183208]

Expected Behaviour The eigenvalues should be random.

Your Environment

QuTiP: Quantum Toolbox in Python
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Current admin team: Alexander Pitchford, Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, Eric Giguère, Boxi Li, Jake Lishman and Simon Cross.
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Previous lead developers: Chris Granade & A. Grimsmo.
Currently developed through wide collaboration. See https://github.com/qutip for details.

QuTiP Version:      4.7.0.dev0+nogit
Numpy Version:      1.21.1
Scipy Version:      1.7.0
Cython Version:     None
Matplotlib Version: 3.4.2
Python Version:     3.8.11
Number of CPUs:     8
BLAS Info:          OPENBLAS
OPENMP Installed:   False
INTEL MKL Ext:      False
Platform Info:      Windows (AMD64)
Installation path:  C:\Users\acer\anaconda3\envs\learning_qutip\lib\site-packages\qutip
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[jakelishman]

QuTiP doesn’t have one built in at the moment, but toqito can do it as numpy arrays, which you can just wrap in Qobj. There’s no scope for density there, though (and it would be very difficult to do so, I think!).

[hodgestar]

Supplying negative or zero eigenvalues in the list and pos_def=True is certainly non-sensical input and should possibly return an error (and I think doesn’t at the moment).