The probability density function (PDF) of a Gaussian (or Normal) distribution centred on the origin in n-dimensional space is given by : p($x$) = B exp[$-\frac{1}{2}x^T\Lambda x$], where $x = (x_1, ... , x_n)$ and $\Lambda$ is an $n$ X $n$ matrix known as the "precision matrix" and B is just a normalising factor.
I understand that the covariance matrix is essentially a measure of how different variables "co-vary" and correlate with one another, but what does the "precision matrix" here mean? Is it a measure of how "co-concentrated" variables are? Furthermore, how would one even arrive to the expression given above... what is the motivation?