If we have a mean $\mu$ and a symmetric covariance matrix $C$ in 2D, they are defined as:

$\mu = \begin{bmatrix} \mu_1 \\ \mu_2 \end{bmatrix}$

$C = \begin{bmatrix} \sigma_{1}^{2} & r \sigma_1 \sigma_2 \\ r \sigma_1 \sigma_2 & \sigma_{2}^{2} \end{bmatrix}$

In a Variational AutoEncoder, it is assumed that there is no correlation between these dimensions. This means that the encoder needs to map each input to mean and variance vectors. As a result, the image will be encoded into two vectors:

1. mu ($\mu$) - the mean point distribution.
2. log_var - the logarithm of the variance of each dimension.

In order to encode an image into a specific point, we can use this formula:

$z = \mu + \exp(log\_var / 2)$