I'm preparing for a test and somewhat noticed I don't understand everything as well as I thought I did.
I'm trying to solve the following problem:
Let be the projection on the plane
(a) Give a basis of consisting of eigenvectors of
Since for all v in V, I guess we can take two orthogonal vectors . But how do we get a third eigenvector? Just taking a third orthogonal vector?
(b) Give the matrix of with respect to the standard-basis in
(c) Is normal?
So since is real I should figure out whether . I guess I should find first.
Any help is appreciated.