Let x. y be nonzero sectors in Rn. n 2. and let A = xyT Show

Question:

Let x. y be nonzero sectors in Rn. n ≥ 2. and let A = xyT Show that
(a) A = 0 is an eigenvalue of A with n - I linearly independent elgenvectors and consequently has multiplicity at least n - 1 (see Exercise 15).
(b) The remaining elgenvalue of A is
λn = tr A= xTy
and x is an eigenvector belonging to λn.
(c) if λn = xTY ≠ then A is diagonalizable.