home   |<<    <--    -->    >>|

Eigensystem symmetry

So, I've taken one of the problem glyphs, for which lambda_1 and lambda_2 are equal. Now, this means that the eigenspace associated with that eigenvalue is two-dimensional. That means that the eigenvectors that we calculate, v_1 and v_2, are not unique.

They might be these two, or these two, or these, or any two vectors in this space-- there is no unique answer. On the other hand, when we calculate the eigenvector associated with the third eigenvalue, that direction is numerically well-defined.

So, the idea is that the mathematical symmetry of the tensor eigenvalues should be reflected in the geometric symmetry of the glyphs geometry that we use to represent the tensors.