Is any one 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?