How to compute Hessian matrix for log-likelihood function for Logistic Regression
Beta is a vector of parameters, therefore:

$
\frac{\delta l(\beta)}{\delta\beta}=
[\frac{\delta l(\beta)}{\delta\beta_1}\quad\frac{\delta l(\beta)}{\delta\beta_2}\quad\frac{\delta l(\beta)}{\delta\beta_3}\quad...\quad\frac{\delta l(\beta)}{\delta\beta_n}]$ and so

$
\frac{\delta(\frac{\delta l(\beta)}{\delta\beta})}{\delta\beta^{T}}=
\begin{bmatrix}
\frac{\delta l^2(\beta)}{\delta\beta_1^2} &amp; \frac{\delta l^2(\beta)}{\delta\beta_1\delta\beta_2} &amp; ... &amp; \frac{\delta l^2(\beta)}{\delta\beta_1\delta\beta_n} \\
\frac{\delta l^2(\beta)}{\delta\beta_2\delta\beta_1} &amp; \frac{\delta l^2(\beta)}{\delta\beta_2^2} &amp; ... &amp; \frac{\delta l^2(\beta)}{\delta\beta_2\delta\beta_n} \\
\vdots &amp; \vdots &amp; \ddots &amp; \vdots \\
\frac{\delta l^2(\beta)}{\delta\beta_n\delta\beta_1} &amp; \frac{\delta l^2(\beta)}{\delta\beta_n\delta\beta_2} &amp; ... &amp; \frac{\delta l^2(\beta)}{\delta\beta_n^2}
\end{bmatrix}$, which is your Hessian.

The term on the right side of your equation is also a matrix, because there is a multiplication of vectors in it: $x_i \cdot x_i^T$, which gives a $n \times n$ matrix.