Algorithm and software for defining the distribution of eigenvalues of random symmetric matrices via simulation

Abstract

A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a uniform random number generator. As a numerical example, the probability that eigenvalues of a certain random symmetric matrix satisfy a given condition is calculated using software implementing the algorithm.

Keywords:

• eigenvalues distribution
• Monte Carlo simulation
• random symmetric matrices
• matlab
• numerical algorithm

2000 AMS Subject Classifications :

• 15A52
• 65C05