KL divergence measures the dissimilarity between two probability distributions. In this problem, you'll implement a function to compute the KL divergence between two multivariate Gaussian distributions given their means and covariance matrices.

Return $D_{KL}(P \,\|\, Q)$ as a Python float, where $P = \mathcal{N}(\mu_p, \Sigma_p)$ is the first distribution (mu_p, Cov_p), $Q = \mathcal{N}(\mu_q, \Sigma_q)$ is the second (mu_q, Cov_q) and $k$ is the dimension:

$D_{KL}(P \,\|\, Q) = \frac{1}{2}\left[\ln\frac{\det \Sigma_q}{\det \Sigma_p} - k + (\mu_p - \mu_q)^\top \Sigma_q^{-1} (\mu_p - \mu_q) + \mathrm{tr}\left(\Sigma_q^{-1} \Sigma_p\right)\right]$