If $\displaystyle\frac{\partial \ell}{\partial \theta_j}=\sum_{k=1}^m(y^{(k)}-h_\theta(x^{(k)})x_j^{(k)}$
where $h_\theta(x)=\theta^Tx, ~\theta,x\in R^n$
$\displaystyle\frac{\partial^2 \ell}{\partial \theta_i \partial \theta_j}=-\sum_{k=1}^m x_i^{(k)}x_j^{(k)}$ ?