Overview
The vector covariance is the covariance of a set of random variables using the language of linear algebra.
Covariance
Covariance is similar to the second moment. It is defined
{% cov(\vec{X}) = \mathbb{E}[(\vec{X}- \mathbb{E}[\vec{X}]) \otimes (\vec{X} - \mathbb{E}[\vec{X}])] %}
where {% \otimes %} is the matrix outer product.
The result is a matrix, where the {% (i, j) %} element of the matrix
is the covariance between the {% i^{th} %} element of {% \vec{X} %} and the
{% j^{th} %} element.