Notation for predicting $\hatβ$ in ridge regression I have been reading around ridge regression and have come across two forms of $\hatβ$ in textbooks. Am I correct in believing that $(X^TX+\lambda I)^{-1} X^TY$ is the same as $RSS + \sum_{j=1}^{p} \beta_j^2$? Also, if they are equivalent, how is the best way to picture this?

The first term is $\hat\beta$ itself, the second term is the objective function that is minimised by it (so the second one is not $\hat\beta$, although required to define it). In fact it's not exactly the objective function, as factor $\lambda$ is missing before the sum (it's the objective function for $\lambda=1$).
