Let be defined by T(p)=xp'. Find eigenvalues of T.
I'm not sure what the notation of T(p)=xp' means and how to go about finding the eigenvalues.
Random Variable showed how to represent this transformation as a matrix- worth knowing for itself.
But for this problem, you don't have to do that. As dwsmith said, if , then . If is an eigenvalue for T, we must have some a, b, c, not all 0, such that . Since that must be true for all x, we can set corresponding coefficients equal: , , and .
If a is not 0, then , if b is not 0, then , and if c is not 0, then .
That is, 0 is an eigenvalue with eigenvectors any multiple of 1, 1 is an eigenvalue with eigenvectors any multiple of x, and 2 is an eigenvalue with eigenvectors any multiple of , exactly what Random Variable got.