We denote by $\lambda _ { 1 }$ (respectively $\lambda _ { N }$) the smallest (respectively largest) eigenvalue of $A$, and we define
$$\Lambda _ { k } = \{ Q \in \mathbb { R } [ X ] \mid \operatorname { deg } ( Q ) \leq k , Q ( 0 ) = 1 \}$$
Show that
$$\left\| e _ { k } \right\| _ { A } \leq \left\| e _ { 0 } \right\| _ { A } \min _ { Q \in \Lambda _ { k } } \max _ { t \in \left[ \lambda _ { 1 } , \lambda _ { N } \right] } | Q ( t ) |$$