  We propose a theory of eigenvalues, eigenvectors, singular values, and
singular vectors for tensors based on a constrained variational approach much
like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are
particularly useful in generalizing certain areas where the spectral theory of
matrices has traditionally played an important role. For illustration, we will
discuss a multilinear generalization of the Perron-Frobenius theorem.
