"You could not live without quaternion, could you?", so was the impression of my advisor.
William Hamilton and William Clifford are my heroes. I fell in love with quaternion some time ago and used it with passion in my dissertation (check the summary). Those who had done extensive polarization analysis using matrix and quaternion would come to the usual conclusion: for this context, quaternion and polarization analysis is a marriage made in heaven.
Now I realize that few days left until 2008 is gone. This would mark my biggest failure for this year. Sadly, I fail (again) to learn Clifford algebra in depth.