Exercises
The following is a series of exercises. Answers to all the exercises are given in the Answers_to_Exercises_Chap15.ipynb Jupyter notebook in the GitHub repository.
- Create a
symmetric matrix 
using the following relationship:
Eq.13
The 
matrix should have its matrix elements drawn from the standard normal distribution with a probability of 0.5, and from the mean-zero unit-variance Laplace distribution in Eq.4, with a probability of 0.5. Calculate the eigenvalues, 
, of and compute the empirical density of scaled eigenvalues 
. Compare this empirical density to the semicircle law in Eq.2.
Tip
You can draw a value 
from the mean-zero unit-variance Laplace distribution by first drawing a value 
from the uniform distribution, 
, then calculating as follows:
Eq.14
Alternatively, you can use the numpy.random.laplace NumPy function to sample the values directly.
2. From the definition of the GUE in Eq.7, generate a GUE matrix and compute its...
