Question is related about reflection definition because I don't understand in what context they say that 'mirror' is
[..] isometries have a set of fixed points (the "mirror") that is an affine subspace [..]
I wish to build a reflection (an isometry) using a a set of fixed points ('mirror') but I don't understand well if I need to start from affine subspace of vector space or from affine subspace of affine space.
Can you provide me an example to build a reflection from a generic fixed points ?
So I wish to understand better also if there is a morphism or some algebraic structure that link directly an affine subspace of vector space with affine subspace of affine space.