In ridge regression using unnormalized features, if you double the value of a given feature A (i.e., a specific column of the feature matrix), what happens to the estimated coefficients for every other feature?
My understanding is that the weight of A is halved, and because of L2 regularization, the concentric circles become ellipses, and all the coefficients associated with other features should all be halved. In the limit of feature scaled to infinity, all the other features become irrelevant (which is why standardization is important).
However, my answer is wrong, and please kindly rectify my reasoning and point out the solution process for the rest of us. Thank you!