The matrix representation of an element in the subalgebra is
the same as its matrix representation in the superalgebra::
- sage: set_random_seed()
sage: x = random_eja(field=QQ,orthonormalize=False).random_element()
sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: y = A.random_element()
works like it does in the superalgebra, even if we orthonormalize
our basis::
- sage: set_random_seed()
sage: x = random_eja(field=AA).random_element()
sage: A = x.subalgebra_generated_by(orthonormalize=True)
sage: y = A.random_element()
We can convert back and forth faithfully::
- sage: set_random_seed()
sage: J = random_eja(field=QQ, orthonormalize=False)
sage: x = J.random_element()
sage: A = x.subalgebra_generated_by(orthonormalize=False)