Derivation
Starting with a random vector {% \vec{Z} %}, we define the mean vector {% \vec{m} %} to be
{% \vec{m} = \mathbb{E}(\vec{Z}) %}
The the covariance of {% A\vec{Z} %}, where {% A %} is a given transformation matrix is
{% cov(\vec{AZ}) = \mathbb{E}[(A\vec{z} - A\vec{m})(A\vec{z} - A\vec{m})^T] %}
{% = \mathbb{E}[A(\vec{z}-\vec{m})(\vec{z}-\vec{m})^T A^T] %}
{% = A\mathbb{E}[(\vec{z}-\vec{m})(\vec{z}-\vec{m})^T]A^T %}
{% = A cov(\vec{z}) A^T %}