Numerical Analysis Of Eigenvalues And Singular Values Distribution Of Random Matrices

Random matrix theory has gradually played an important role in many subjects.This article mainly talks about the eigenvalues and singular values distribution of ran-dom matrices.And we focus on three kinds of matrices:Gaussian orthogonal ensem-bles,Gaussian unitary ensembles and Ginibre ensembles.First we give some fundamen-tal laws of random eigenvalues distribution.Building upon these results,we simulate the distribution using Mathematica.Furthermore,we increase the order and the mul-tiplications of matrices.And we simulate the circumstance using mathematica again.We draw the painting of the eigenvalues distribution of high-dimension random matri-ces.The simulation of this article directly validates the correctness of some distribution laws.We also discuss the eigenvalues distribution of m matrices of order n.When changing the values of m and n,we can observe a lot of interesting phenomena.