Principal-component shrinkage by ridge regression

For $X^{T}X=V\Lambda V^T$, ridge regression multiplies the fitted response along the $i$th normalized sample principal component by the shrinkage factor ${\Lambda }_{ii}/({\Lambda }_{ii}+\lambda )$. Directions with variance much larger than $\lambda$ are nearly retained, while directions with variance much smaller than $\lambda$ are nearly removed.