Given a symmetric, positive semi-definite matrix $M$ with $p$ dimensions, and its eigenvalues are $\lambda_1=\lambda_2>...>\lambda_p$, how to show that the corresponding eigenvectors $u_1$ and $u_2$ are not unique and span 2-dimensional subspace?
let $U = (u_1, u_2,...,u_p)$, $D = $diag$(\lambda_1,...,\lambda_p)$, then we have $M = UDU^\intercal$, and due to orthogonality of $U$, we have $D = U^\intercal MU$, and satisfies $u_1^\intercal Mu_1=u_2^\intercal Mu_2$.
Also, we know that $u_1^\intercal u_1=u_2^\intercal u_2 = 0$, as well as $u_1^\intercal u_1 = u_2^\intercal u_2 =0$. I just don't know how to make use of these relations... Any ideas??