I think either JSON or something binary is fine, perhaps both. One of the complaints that we get when the summary of a covariance matrix, Sigma, is printed is that you see the same summary for Sigma[1,2] as for Sigma[2,1] because it is a symmetric matrix. So, a better summary would only show that once. Furthermore, there is no need to summarize the fact that the diagonal of a correlation matrix is always 1 or that the upper triangle of a Cholesky factor is always zero. But we need to know what type of matrix the thing is to do that.