Probability Tensor and Ellipsoid

ehrenfest

Hey, I asked this question in another post, but I realized I may have posted it in the wrong place: http://www.physicsforums.com/showthread.php?t=179495

So, is anyone familiar with the concept of a probability ellipsiod which represents a probability tensor whose principal components must sum to 1?

My question is why must they sum to one? Does this mean that the magnetic field (in this context) must be along one of those axes?