"""
B = self.parent().natural_basis()
W = self.parent().natural_basis_space()
+
+ # This is just a manual "from_vector()", but of course
+ # matrix spaces aren't vector spaces in sage, so they
+ # don't have a from_vector() method.
return W.linear_combination(zip(B,self.to_vector()))
sage: (J0, J5, J1) = J.peirce_decomposition(c1)
sage: (f0, f1, f2) = J1.gens()
sage: f0.spectral_decomposition()
- [(0, 1.000000000000000?*f2), (1, 1.000000000000000?*f0)]
+ [(0, f2), (1, f0)]
"""
A = self.subalgebra_generated_by(orthonormalize_basis=True)