The RV coefficient is like a correlation between several variables. In R I found so far several methods that seems to calculate it:

FactoMineR::coeffRV

subselect::rv.coef

MatrixCorrelation::RV

However the rv.coeff function from the subselect package works with only one matrix, and the coeffRV and the RV functions differ in they results.

This lead me to search for its definition. All the papers mention Escoufier as the originator of these idea. The longest citation (and more relevant) can be found on a preprint, where it is mentioned the year, the author and that several of these papers are in French.

In this document we can find the definition which is only followed by the RV function, in the coeffRV function the values are scaled.

You can check that:

RV(scale(X, scale = FALSE), scale(Y, scale = FALSE)) == coeffRV(X, Y)$rv