Figure 2. Graphical depiction of the eigentensor decomposition of covariance matrices A, B and C.

The mean matrix M is estimated within the non-Euclidean space of symmetric positive-definite matrices; the transformation $f(X)=\mathit{Log}(M^{-\frac{1}{2}}{\text{XM}}^{-\frac{1}{2}})$ maps A, B and C into an Euclidean space centered on M. Only in this Euclidean space are the eigentensors (PM1 and PM2) estimated.