HadamardEJA could be equipped with an inner- product that is twice
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?
+
+9. Pre-cache charpoly for some small algebras?