Properties of Eigenvalue/Eigenvector of Hypermatrices

Key Points

• This research aims to explore and establish three fundamental properties of universal eigenvalues and eigenvectors of hypermatrices.
• Proved properties of eigenvalues/eigenvectors from hypermatrices including the Kronecker product.
• Defined similarity of hypermatrices and its impact on eigenvalues/eigenvectors.
• Examined the Cayley–Hamilton theorem as it applies to hypermatrices.
• Proved that the eigenvalue/eigenvector of the Kronecker product is derived from the product of the corresponding factor hypermatrices.
• Established that similarity in hypermatrices guarantees identical eigenvalues and eigenvectors.
• Detailed the Cayley–Hamilton theorem specifically for hypermatrices.

Abstract