Is it possible to find eigenvalues and principal directions for a 4th order tensor? How?

For a zero order tensor? for a first order tensor? for a third order tensor.........

many thanks

Checking the iMechanica web, I notice some discussion about the Cauchy stress tensor, whether it is covariant or contravariant.  Well, a tensor is neither covariant nor contravariant, while it can be expressed by its covariant, contravariant, or mixed *components* with respect to any arbitrary coordinate system. See the attached short explanation.

Some of you probably work on problems that involve moderately large strains. An useful strain measure for such problems in the logarithmic or Hencky strain. In particular, if you deal with the numerics of large strain simulations, you will often need to compute the material time derivatives of logarithmic strains.