  A cubic hypermatrix of order $d$ can be considered as a structure matrix of a
tensor with covariant order $r$ and contra-variant order $s=d-r$. Corresponding
to this matrix expression of the hypermatrix, an eigenvector $x$ with respect
to an eigenvalue $\lambda$ is proposed, called the universal eigenvector and
eigenvalue of the hypermatrix. According to the action of tensors, if $x$ is
decomposable, it is called a universal hyper-(UH-)eigenvector. Particularly, if
all decomposed components are the same, $x$ is called a universal diagonal
hyper (UDH-)eigenvector, which covers most of existing definitions of
eigenvalue/eigenvector of hypermatrices. Using Semi-tensor product (STP) of
matrices, the properties of universal eigenvalues/eigenvectors are
investigated. Algorithms are developed to calculate universal
eigenvalues/eigenvectors for hypermatrices. Particular efforts have been put on
UDH- eigenvalues/eigenvectors, because they cover most of the existing
eigenvalues/eigenvectors for hypermatrices. Some numerical examples are
presented to illustrate that the proposed technique is universal and efficient.
