First off, fantastic article. Thank you.
So I believe there is a tiny error here, but I'm not quite sure...
In the following comment
"The off-diagonal elements being equal to 0 means that the variables in the data are uncorrelated; the diagonal elements all being equal to 1 means that the sum of each squared variable would equal 1. That would be true if the variables each had mean 0 and variance 1/N. Such data may not be common, but I can imagine them."
So the uncorrelated off-diagonals means that cov(x_i, x_j) = 0 when i != j, which I agree with.
When i = j we are looking at cov(x_i, x_i) = var(x_i) = 1. This means that the variance is 1 for *each* variable, but the variance of the mean is 1 / N from
Bienaymé formula.
https://en.wikipedia.org/wiki/...
Also, how do you know that the mean is 0? I'm not saying it's not, I just wan't able to convince myself of that at a glance. Thanks!