Let $A \in \mathbb{R}^{m \times n}$ be of full rank. Consider $X_{k+1}=(2k-X_{k}A)X_{k}$, $X_0 = \alpha A^{T}$.
Let $E_k = I-X_kA$,
Deduce that if $||E_{0} ||_{2}<1$, then $lim_{k \rightarrow \infty}E_k=0$,
I'm thinking it's something like this $||E_0||_{2} = max_{v \not = 0} ||E_{o} v || / ||v|| < 1$, therefore
$max_{v \not = 0} ||E_{0} v || < ||v||$.
Then maybe use the fact that $E_k = E_0^{k-1}$.
But, I'm stuck here.
