Given the formula of Mahalanobis Distance:
D^2_M = (\mathbf{x} - \mathbf{\mu})^T \mathbf{S}^{-1} (\mathbf{x} - \mathbf{\mu})
If I simplify the above expression using Eigen-value decomposition (EVD) of the Covariance Matrix:
S = \mathbf{P} \Lambda \mathbf{P}^T
Then,
D^2_M =...