\begin{align*}
        |\hat{A}_1| &= |B-\hat{z} w^T + F| \leq |B| + |\hat{z}||w|^T + \underbrace{|F|}\\
            &\leq |B| + |\hat{z}||w|^T + \overbrace{2\eps(\underbrace{|B| + |\hat{z}||w|^T}) + \bigo(\eps^2)}\\
            &\leq(1+2\eps)(|B|+|\hat{z}||w|^T) + \bigo(\eps^2)\\
        |H_1+F| & \leq |H_1| + |F|\\
                & \leq 3(n-2) \eps(|\hat{A}_1| + |\hat{L}_1| |\hat{R}_1|) + 2\eps(|B| + |\hat{z}||w|^T) + \bigo(\eps^2)\\
                & \leq 3(n-2) ((1+2\eps)(|B|+|\hat{z}||w|^T) + |\hat{L}_1||\hat{R}_1|) + 2\eps(|B| + |\hat{z}||w|^T) + \bigo(\eps^2)\\
                & \leq 3(n-1_ \eps(|B| + |\hat{z}||w|^T + |\hat{L}_1| |\hat{R}_1|) + \bigo(\eps^2)
    \end{align*}
    und damit
    \begin{align*}|H| &= \left[ \begin{array}{cc} 0 & 0 \\ \underbrace{|\alpha f|}_{|\alpha||f|} & |H_1+F| \end{array} \right] \leq \left[ \begin{array}{cc} 0 & 0 \\ \eps|v| & 3(n-1)\eps(|B|+|\hat{z}||w^T| + |\hat{L}_1||\hat{R}_1|) \end{array} \right] + \bigo(\eps^2)\\
    &\leq 3(n-1) \eps \left[ \begin{array}{cc} 0 & 0 \\ |v| & |B| + |z||w|^T + |\hat{L}_1||\hat{R}_1| \end{array} \right] + \bigo(\eps^2)\\
    &\leq 3(n-1) \eps\left(\underbrace{\left[ \begin{array}{cc} |\alpha| & |w|^T \\ |v| & |B| \end{array} \right]}_{=|A|} + \underbrace{\left[ \begin{array}{cc} 1 & 0 \\ |\hat{z}| & |\hat{L}_1| \end{array}\right] \left[ \begin{array} |\alpha| & |w|^T \\0 & |\hat{R}_1| \end{array}\right]}_{=\left[ \begin{array}{cc} |\alpha| & |w|^T \\ |\hat{z}| |\alpha| & |\hat{z}||w|^T + |\hat{L}_1| + |\hat{L}_1||\hat{R}_1| \end{array}\right]}
    \end{align*}