Hi all, I was studying for a Math test until this question stumped me:
Let be an inner product space and be a self-adjoint linear transformation such that .
a) Show that all eigenvalues of are either 0 or 1.
b) Describe the eigenspaces of in terms of the kernel of , the range of and .
So for question a) I know that a self-adjoint linear transformation means and where is a scalar but I don't know how to use these to solve the question...
As for b) I know that Nullity T + Rank T = Dim V which is equivalent to dim(ker T) + dim(im T) = dim V ...but I guess I can't solve this until I know how to do question a)...
Any help would be greatly appreciated.