Identity matrix 与whitening的理解

A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1.[1] The transformation is called "whitening" because it changes the input vector into a white noise vector.
Identity matrix本以为是一个不变的矩阵；以至于无法理解白化；