Getting Started with Random Matrices: A Step-by-Step Guide | Hacker News Reader

Getting Started with Random Matrices: A Step-by-Step Guide

medium.com

39 pointsjorgenveisdal11 comments

Look, I'm actually interested in the topic, and this piece actually seems to have some useful information in it, but please please please, stop publishing technical/math-heavy articles on Medium. Putting pictures of equations mid-text combined with occasionally cut-off or accidental multi-line equations kills the readability. I mean, the author already spent the time putting most of the background into a Jupyter notebook, which is much more accessible and readable, even directly in the Github repository [1].

I would love to see Medium adjust their formatting to make it possible for something like Tables of Contents, or faithful rendering of notebooks that don't just rely on Github gists, but until then, I think it does a huge disservice to the actual information that technical/symbolic-math-including authors are trying to convey.

[1] https://github.com/WessZumino/Random-Matrix-theory-for-pedes...

I'll go even further: please stop posting articles on Medium, ever, because they have paywall which prevents many of us from reading them (and they profit off the author's labor).

For any quantitatively-oriented person, the quickest solution might be to write the article in LaTeX and host it on github.io, but other solutions are of course possible (e.g. MathJax and some other free web hosting).

For paywalled sites that let users read X free articles, the easiest solution for me was to block all cookies from the site, i.e. block all cookies from [*.]medium.com. Medium will always think that "You have 2 free member-only stories left this month". This has worked for nytimes and medium so far.

Always wondering: when will this fall under some law of 'computer assisted fraud' or so.

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.

I used to publish some math-heavy posts on medium (complete with equation images!) before moving it all over to gitlab pages with the hugo static site generator, and equations rendered with katex. If the author is reading this, the translation process didn't take very long (maybe a day) and I'm very happy with the results; compare:

https://medium.com/@ahelwer/walking-the-faster-than-light-ti...

https://ahelwer.ca/post/2018-12-07-chsh/

I'm generally allergic to tweaking things & general command-line bullshit but the whole process was surprisingly smooth. Readers don't have to deal with popup & tracker bullshit (except for youtube, who have endeavored to make it impossible to embed videos with issuing tracking cookies), and it feels nice to have much more control over what makes it into the final product.

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.

@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.

The statement about general matrix diagonalisation is not true (not every matrix is similiar to a diagonal matrix, take nilpotent matrix as counter example).

For random matrice the author introduces what it means to be rotationally (O) invariant, but is what follow restricted to that? Also it is not too clear why the code is actually doing (creating the same ensemble) as what was talked about before.

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.

Thanks. By saying 'NxN matrices from a Gaussian distribution' you mean each entry of the matrix is a sample of a Gaussian distribution, right? At least this is what the code is doing(there could be other meanings to this term)

Reply on news.ycombinator.com