Question:
Theory regarding diagonalization
1. Refer to the linear operator T: R3 -> R3 defined by T (x1, x2, x3) = (x1 - 3x3, x1 + 2x2 + x3, x3 - 3x1).
2. Determine whether or not there is a basis F for R3 relative to which the transformation T can be represented by a diagonal matrix
D = [T]F.
3. If there is, show that D is similar to the standard matrix representation [T]E for T.
If not, why?
(Note that I've already found eigenvalues of 2, 4 and -2.)