I am unclear as to how some scalars have been calculated. I know what the two vectors and the inverse covariance variance matrix are but please could you clarify the operations required to compute into a single number? There is also a set of data on page two that needs computing along with a general explanation of how to do it. If you are a Matlab or a Mathematica user then such a script would be helpful for me along with general explanations.
This provides examples of working with correlation structure and covariance matrix to calculate scalars.