# Correlation between two distances (distance matrixes)?

Premise: I have a dataset of elements for which I have a representation in 2 different spaces, a "latent" space and the original space (I can move between those with an Autoencoder neural network).

I want to prove a conjecture where I think that a distance that I developed for the original space doesn't "correlate" with the euclidean distance in the latent space. (By correlate I mean that I feel that "close" elements in one space are "distant" in the other, by their respective distances)

I have computed the distance matrix for both the distances, each in its relative space, for each pair of samples in the dataset.

How do you suggest I can prove this or verify it?

If you use Python you can use scipy.stats.pearsonr(x, y) to do so, where is x is the distance matrix for one of the spaces and y the other.