principal strains using eig function

I am trying to use the eig function to calculate the principal strains from 3D strain tensor. Unfortunately I do get different results than from another tool (<http://www.continuummechanics.org/cm/techforms/Eigen.html>) For

A1 = [4.420000000000000   1.350000000000000   3.509000000000000;
1.350000000000000   3.832000000000000                   0;
3.509000000000000                   0   3.207000000000000]

Matlab eig function yields

    >> [V1, D1] = eig(A1)
    V1 =
      -0.651153549926562   0.054428335246106   0.756991816825237
       0.232116359059687  -0.935349177129471   0.266915553499784
       0.722579442189515   0.349513194551449   0.596422230101738
    D1 =
       0.044859378106921                   0                   0
                       0   3.753442970840320                   0
                       0                   0   7.660697651052759

while the Web tool gives:

The Values look pretty the same, but their position in vector/matrix is different. As far I understand, the columns of the V1 represent the cosines of the angle between the a principal strain and the Cartesian axis. But which corresponds to which principal strain and how to calculate angles between the principal strains and the Cartesian strain axis?

Answer 1

[Eric Lin]

What is happening is the web app is displaying the eigenvectors by row whereas MATLAB is displaying them by column. The relative order of the eigenvectors is not significant.

I am not familiar with the domain but from a quick search it seems that the vectors are related to the strains based on their eigenvalue, i.e. the max principal strain is the eigenvector with the largest eigenvalue. Again, I am not familiar with the domain but angles between vectors can be computed by dot product.