random_matrix_eigenvalues

random_matrix_eigenvalues, a Python code which demonstrates how, for certain probability density functions (PDF), a symmetric matrix with entries sampled from that PDF will have eigenvalues distributed according to Wigner's semicircle distribution.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

random_matrix_eigenvalues is available in a Python version.

Related Data and Programs:

test_matrix, a Python code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.

Reference:

1. John D Cook,
   Fat-tailed random matrices,
   https://www.johndcook.com/blog/2017/01/29/heavy-tailed-random-matrices/
   Posted 29 January 2017.

Source Code:

• random_matrix_eigenvalues.py, the source code.
• random_matrix_eigenvalues.sh, runs all the tests.
• random_matrix_eigenvalues.txt, the output file.