variational bayes derivation in Pattern Recognition and Machine Learning

Hi,

I hope someone can help me with understanding some derivation.

The solution to exercise 10.13 in the Pattern Recognition and Machine Learning book derives the update equation for the posterior distribution on mean (mu) and precision (Lambda) of a Gaussian component in a Bayesian GMM.

page 75 in http://research.microsoft.com/users/cmbishop/PRML/prml-web-sol-2007-08-03.pdf

After some algebraic manipulation, it reaches the stage where the log of the posterior distribution on mu given Lambda, is a quadratic form depending on mu. The solution then says that this shows that the posterior is a Gaussian and its mean (m) and precision (beta*Lambda) can be found by completing the square.

I am confused as to what happened to the other quadratic part (the one involving the square of m), is it ignored because it does not involve mu? Or have I missed something.

Also how does the determinant of the precision factors into all of this or is it ignored too?

thanks for any help.

Shaobo
.