Structured matrix eigenvalue clusters

eigclusters

%params
N = 512;
k = 128;
p = .5;
%form block clustered matrix
A = rand(N,N)>p;%or randn(N,N) also
B = diag([50*ones(1,k)  1*ones(1,N-k)]);
C = A+B;

%compute spectrum
E = eig(C);

%plot stuff
figure(1)
subplot(211)
imagesc(C)
subplot(212)
plot(E,'o')
axis(equal)