The Elements of Statistical Learning says on page 113:
Sphere the data with respect to the common covariance estimates $\hat{\Sigma}$: $X^* \leftarrow D^{-1/2}U^TX$ where $\hat{\Sigma} = UDU^T$. The common covariance estimate of $X^*$ will now be the identity.
Can someone help me understand why $X^* \leftarrow D^{-1/2}U^TX$ spheres the data?