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What you want to do is not necessarily impossible, but it is unlikely, and harder than you think. First of all, you seem to underestimate what it takes to become a researcher. There is no uniform rule, as there are wildly different levels of talent, and also different areas require different levels of expertise to be able to produce research. That said, a ...


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Based on the discussion in the comments, it seems that what is really needed is code that will produce the eigenvalues of the matrix $D_N$. We can produce this outcome with the following script: N = 2^3; D = circshift(eye(N),-1) + circshift(eye(N),1) - 2*eye(N); eig(D)


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