Another formulation of this which I like is that the Mahalanoubis distance measures “how many standard deviations apart” two state vectors are. Note that since

Another formulation of this which I like is that the Mahalanoubis distance measures “how many standard deviations apart” two state vectors are. Note that since the covariance matrix has variance on the diagonal, it corrects not only for correlations but also normalizes each dimension using their standard deviation.