Exercise 6.13: Bernstein's Inequality for Vectors

chapter 6

(a)

Follows from $\rank(V_n) = \rank(\Sigma) + 1$.

(b)

Simply note that \begin{equation} \tr(V_n) = 2 \tr(\Sigma), \quad \norm{V_n}_2 = \tr(\Sigma). \end{equation}