I have read that to apply ridge regression, we first need to standardize the predictive variables. That is because the variables should be in a homogenous scale so that lambda has an effect of the same magnitude on all of them.
However, taking a look at the ridge regression implementation of the scikit-learn library, I see that the X variables are centered but not standardized. That is, the variables retain their scale.
I was wondering if you know why that is, and when is each technique (standardization vs centering) advised.