Girko's Circular Law

Author

Eric W. Weisstein
February 14, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/GirkosCircularLaw.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GirkosCircularLaw.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Plot

Girko[n_,cnt_]:=Module[{p=Flatten[Eigenvalues/@RandomReal[NormalDistribution[],{cnt,n,n}]]/Sqrt[n]},
Graphics[{
{Red,PointSize[.005],Point[{Re[#],Im[#]}]&/@p},
Text[TraditionalForm[ToString[n]<>"×"<>ToString[n]],{0,-1.9}]
},PlotRange->{1.8{-1,1},{-2.1,1.8}}
]
]

Girko[50,500]//Timing//AbsoluteTiming

GraphicsGrid[{
Table[Girko[n,1000],{n,2,5}],
Table[Girko[n,500],{n,20,50,10}]
}]