What would currently be the best way to share a matrix with the math community?
(I'm aware of Matrix Market but it seems the last update was in 2007...)
If it happens to be sparse, you might also consider the UF collection:
I don't know that it's especially active in the last few years, a cursory search seemed to suggest the last additions were around 2013 or so.
Most languages have the ability to read HDF5 files in some fashion. That would be a very cross-compatible way to save a sparse matrix to a file to share.