the usual one. Then for the basis to be orthonormal, we would need
to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.
-8. Use charpoly for inverse itself?
+8. Pre-cache charpoly for some small algebras?
-9. Pre-cache charpoly for some small algebras?
+9. Compute the scalar in the general natural_inner_product() for
+ matrices, so no overrides are necessary.
+
+10. Eliminate "natural representation" for non-matrix algebras.
+
+11. The main EJA element constructor is happy to convert between
+ e.g. HadamardEJA(3) and JordanSpinEJA(3).