Principle eigenvectors and cross product of mouse difusion tensors.

Previous post had a wrong method, the values used were not the principle eigenvectors. 

Diffusion matrix is upper symmetric,
[Dxx Dxy Dzy
  0      Dyy Dyz
 0       0      Dzz]

=

[Dxx Dxy Dzy
 Dyx Dyy Dyz
 Dzx Dzy Dzz]
             

so when w take the eigenvectors and values in MATLAB with

matr[u v]=eig(D)

we get a 3x3 matrix of eigenvalues u
and a 3x3 matrix of eigenvectors v

u is a diagonal matrix and the elements are the eigenvalues

v is a matrix of 3, 3x1 column vectors which are the principle eigenvectors of D

To take the cross product, we should take the cross product of each principle eigenvector with the corresponding eigenvector extracted from the diffusion matrix at the next time point.

So to get the matrix of the cross products, we will need to take the cross product three times for each pair and form this into a new matrix, unless there is a quicker command.