How does one plot eigenvalues distribution of a large matrix? I want to plot the distribution to show that the set of eigenvalues of the matrix of current interest is symmetric with respect to the imaginary axis.


Perhaps this is what you need?

r = RandomReal[{0, 1}, {1000, 1000}];
ev = Eigenvalues@r;
ListPlot[{Re@#, Im@#} & /@ ev, AspectRatio -> 1, ImageSize -> 300, 
 PlotRange -> 10*{{-1, 1}, {-1, 1}}, AxesLabel -> {"Re", "Im"}]

enter image description here


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