A+\sqrt{5}I induces thus an Euclidean structure on the quotient space \mathbb R^6/\ker(A+\sqrt{5}I) which is isomorphic to \mathbb R^3 since the kernel \ker(A+\sqrt{5}I) of A+\sqrt{5}I has dimension 3. The image under the projection \pi:\mathbb R^6 \longrightarrow \mathbb R^6/\ker(A+\sqrt{5}I) of the six coordinate axes \mathbb R v_1,\dots,\mathbb R v_6 in \mathbb R^6 forms