sage: (J0, J5, J1) = J.peirce_decomposition(c1)
sage: (f0, f1, f2) = J1.gens()
sage: f0.spectral_decomposition()
- [(0, c2), (1, c0)]
+ [(0, 1.000000000000000?*c2), (1, 1.000000000000000?*c0)]
"""
A = self.subalgebra_generated_by(orthonormalize=True)