Probability Ellipsoid: Explaining Magnetic Field Axes

[ehrenfest]

Is anyone familiar with the concept of a probability tensor or a probability ellipsoid? I am learning about them in the context of NMR techniques.
Here is a page describing them: http://www3.interscience.wiley.com/cgi-bin/abstract/107633228/ABSTRACT?CRETRY=1&SRETRY=0

My question is, why would the principal values need to add up to 1? The principal values are the probability that the magnetic field points along that axis, so does the requirement that they add up to one mean that the magnetic field can only point along the three axes of the ellipsoid? Why can it not point anywhere else?

 

[Gokul43201]

The link doesn't work for me.

 

[chemisttree]

Since you are dealing with probability, it seems natural to consider that the probability of allowable states should sum to 1. The question you have is, "Why are there only a limited number of allowable states?" I believe that the tensor definition is of the net magnetization vector. The definition itself only deals with the vector sum of all allowable magnetization vectors. The ellipsoid should deal with some variablility about the net magetization vector itself either before or after some pertubation.