Exercise 4.10.1

$D=\left[\begin{array}{ccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 6\hfill \\ \hfill 1\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill 6\hfill & \hfill 1\hfill & \hfill 0\hfill \end{array}\right]$and $d_1=\left[\begin{array}{c}\hfill 0\hfill \\ \hfill 1\hfill \\ \hfill 6\hfill \end{array}\right]$, according to equation (4), we have $G=\left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 3\hfill & \hfill 6\hfill \end{array}\right]$, This is not positive semidefinite, because its eigenvalues are ${\lambda }_1=0$, ${\lambda }_2=\frac{7+\sqrt{61}}{2}$ and ${\lambda }_3=\frac{7-\sqrt{61}}{2}<0$