Restriction of Linear Operator

I am doing some self-study out of a Linear Algebra text.
I am trying to prove one of the questions and it seems obvious so I
wonder if I am missing something.

The question asks to prove
Given a operator T on the vector space V, and a T-invariant subspace W
that an eigenvector of Tw (restriction of T to W) is also an
eigenvector of T and
has the same eigenvalue.

However I thought the restriction of T was just limiting the domain to
W so that Tw(v) = T(v) for v in W. What more is there to say?

.