Calculate and display the eigenvalue spectrum of real symmetric square matrices using numpy and matplotlib. Execute and/or answer the following tasks/questions: 1. Constract a large real square matrix...

Calculate and display the eigenvalue spectrum of real symmetric square matrices using numpy and matplotlib.
Execute and/or answer the following tasks/questions:
1. Constract a large real square matrix with matrix elements independently (random) drawn from a normal distribution with mean $\mu=0$ and standard deviation $\sigma=1$. A large NxN matrix should have at least N>100, but N=1000 or more is better.1. Calculate the eigenvalues of ths matrix. What is the smallest and the largest eigenvalue and how do they depend on the size of the matrix $N$? Plot this dependence. Calculate the mean of the eigenvalues.1. For the reminder of this project, set the diagonal elements of your matrix to zero. This will ensure that the mane of the eigenvalues is zero and the eigenvalue spectrum is centered around zero.1. Create a histogram of the distribution of the eigenvalues. Can you guess the distribution function? It is known as the Wigner semi-circle law.1. Calculate the spacing of the eigenvalues and display the distribution of the eigenvalue spacings in an appropriate figure.1. How do your results change when you draw the matrix elements from a uniform distribution instead?
The PDF (probability density function of the normal (Gaussian) distribution is given by