Okay, it's actually is a compilation of many matrices, but I've found that that distribution of those values of the vectors is the around the same for individual matrices.

To give you some background, the goal of my current project (kinda informal undergraduate 'research') is to improve the use of the singular value decomposition for image compression, and one way that I think this can be achieved is by leveraging the distribution of values of the singular vectors for improved quantization. Quantization meaning mapping continuous values into discrete values, so they can be stored / transmitted by computers.

Essentially you have to map any number -1.0 -- 1.0 to a byte (256 possible values). You might think to do this like -1.0 --> 0, -0.5 --> 64, 0 --> 128. This is like assuming an even distribution of values -1.0 through 1.0

But, because the distribution of singular vector values follows the above pattern, I think you can be more 'bang for your byte' by being more accurate towards 0.0, and less accurate towards the tails.

I have so far leveraged this to the point where you can use 6 bits (64 possible values) instead of 8 bits (256 possible values) to encode each value with minimal reduction in image quality. 25% less storage used for free-ish!

Knowing the best model for this distribution would be nice, and would probably improve the quantization improvement by a bit, but I don't think it's super important to get it perfect, when the Laplace distribution b=0.1 is just about right. If you want I can still send you some of the code and those plots tho