Fig. 1.

Left: the symmetric matrices $e_{ab}^{(1)}$, $e_{ab}^{(2)}$, $e_{ab}^{(3)}$ (red) and $e_{ab}^{(1)}+e_{ab}^{(3)}$, $e_{ab}^{(2)}+e_{ab}^{(3)}$ (blue) as vectors in ${\mathbb{R}}^3$. The positive semi-definite matrices correspond to vectors which are inside/above the indicated cone (including the boundary). Right: the fourth order tensors $(e_{ab}^{(1)}+e_{ab}^{(3)})(e_{cd}^{(1)}+e_{cd}^{(3)})$ and $(e_{ab}^{(2)}+e_{ab}^{(3)})(e_{cd}^{(2)}+e_{cd}^{(3)})$ depicted in blue, and $e_{ab}^{(3)}{e}_{cd}^{(3)}$ shown in red are viewed as quadratic forms and illustrated as ellipsoids (made a bit ‘fatter’ than they should be for the sake of clarity)