bline80

@qchris, thanks for your comment. I agree Medium is a bit of a pain for math. Equations cutout are not too bad in my opinion, they are mostly time consuming to make. Looking at the final result I do not see how readability is affected. I would say that inline math is the worst and may in this case affect readability.

The information in the Jupiter notebook is different than the one in the article; actually I find math in Jupiter Notebooks also not nice and readable, apart from the occasional equations here and there... for a full calculation it is not the best, even though some extensions help.

Sure, but this gives little visibility and it will be skewed versus a particular audience. ArXiv is a better alternative then, but again it restricts the audience.

Btw, I thought the article was not behind a paywall ... I chose not to profit from it by not activating the option. I need to check again how it works.

Thanks Andrew. Yes Medium is not that good for math, but it gives visibility to a broader audience w.r.t. a personal page. The plan was to add the PDF of the article on GitHub but I forgot. Nevertheless, beside the painful process of cutting and converting equations, the final result is not too bad in my opinion.

Hi Andi, thanks for your comment, I just found out about this. Actually I did not write that any matrix can be diagonalised. I wrote that we are dealing with matrices that can be diagonalised via an orthogonal transformation. Indeed, I also specify (in the notebook is quite clear) that we are working with real symmetric matrices, and these can be diagonalised via orthogonal transformations:

https://en.wikipedia.org/wiki/Diagonalizable_matrix#Diagonal...

This is why is called the Gaussian Orthogonal Ensemble. The Unitary ensemble deals with unitary matrices for example. All of these ensembles deal with diagonalisable matrices.

The code is providing a numerical verification of the analytical formula. It is a simple code that samples symmetric matrices of different NxN size from a Gaussian distribution.

For N fixed, you draw a certain number of samples and you plot the eigenvalue distribution and compare it with the analytics. Then you can see that for small N there is a deviation from the analytical expression, as this was formally obtained in the large N limit.

Hope this clarifies.