2B17 Eigenvalues and Eigenvectors of A Tensor

If is a tensor, and is a vector, then if

then  is an eigenvector, is the corresponding eigenvalue,

If   is a unit eigenvector, then

  Let , in terms of components,

or

  are direction cosines of the vector, then

We have a unique vector (eigenvector) for each eigenvalue.

Eigenvalues cntd.