Miguel,

Having read #8974 carefully, I could see the default for endomorphisms
going either way.  My main concern is that matrices follow practice
and default to providing eigenvalues (and eigenvectors) outside the
base field.  Endomorphisms could default to behave identically to
matrices, or they could respect the notion of being functions and only
return "proper" elements of the domain and range, as you have argued
in regards to your own teaching.  But with options available for
matrices and endomorphisms, individual opinions/tastes can be
accomodated.

Thanks for bringing the discussion to sage-devel.

Rob

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