Hi Rick, thanks for the interesting article. This is indeed a beautiful and useful result. I have a question regarding the existence of the inverse of X'X - x_i'x_i. If we assume that X has full column rank then clearly X'X is invertible, but what about X'X - x_i'x_i? As stated in the Sherman-Morrison theorem, the inverse exists if and only if x_i(X'X)^{-1}x_i' is not equal to 1. Is there any reason why we can expect this to be true? Hoping you can shed some light on my question. Thanks.