Question

Show that ~v:~ has eigen values 1, and the projectors onto the corresponding eigen spaces are

Answer 1

Answer:

tried to first let B=(b1,...,br) be an orthonormal basis of E. By the projection formula, we will have (let T be the projection mapping):

T(v)=∑i=1r(v,vi)vi

Then I tried finding the transformation matrix T such that T(v)=Tv (say in the standard basis), but I haven't had any luck finding the transformation matrix (which would then allow us to compute the respective eigenvalues and eigenspaces). I was thinking of perhaps choosing the respective basis to B and then completing it to a basis of V (say Steinitz' Lemma), but I'm not sure if this is the way to proceed.