+ Our natural basis is normalized with respect to the natural inner
+ product unless we specify otherwise::
+
+ sage: set_random_seed()
+ sage: n = ZZ.random_element(1,4)
+ sage: J = QuaternionHermitianEJA(n)
+ sage: all( b.norm() == 1 for b in J.gens() )
+ True
+
+ Since our natural basis is normalized with respect to the natural
+ inner product, and since we know that this algebra is an EJA, any
+ left-multiplication operator's matrix will be symmetric because
+ natural->EJA basis representation is an isometry and within the EJA
+ the operator is self-adjoint by the Jordan axiom::
+
+ sage: set_random_seed()
+ sage: n = ZZ.random_element(1,5)
+ sage: x = QuaternionHermitianEJA(n).random_element()
+ sage: x.operator().matrix().is_symmetric()
+ True
+