Let and define as the 90-degree rotation operator given by where are the components of a vector in V.
a- show that T is normal
b-T does not have any eigenvalues in R.
For a), find the matrix which represents with respect to the standard basis. Then show that the matrix is normal.
For b), suppose that . What can you tell about ? (Equivalently, find the roots of the characteristic polynomial of the matrix you found in part a) ).