using LinearAlgebra
A=rand(5,5) .- 0.5
println("A random matrix:")
display(A)

println("\nThe eigenvalues are:")
display(eigvals(A))

AA=copy(A)
for k=1:10000
    global AA
    z=qr(AA)
    AA=z.R*z.Q
end
println("\nThe QR algorithm might lead to blocks which")
println("correspond to complex conjugate eigenvalues")
display(AA)

# shifted version
AA=copy(A)
for k=1:10000
    global AA
    z=qr(AA-0.5im*I)
    AA=z.R*z.Q+0.5im*I
end
println("\nShifting by an imaginary offset hopefully gives")
println("all the eigenvalues on the diagonal")
display(AA)

println("\nHere is just the diagonal")
display(diag(AA))