Proves three properties of eigenvalues and eigenvectors of hypermatrices, suggesting their significance in mathematical analysis.
Three properties of the universal (U-) eigenvalues/eigenvectors of hypermatrices are proposed and proved. (1) The eigenvalue/eigenvector of Kronecker product of hypermatrices is the product of eigenvalues/eigenvectors of factor hypermatrices. (2) The similarity of hypermatrices is defined, and then it is proved that the similarity ensures the same eigenvalues/eigenvectors. (3) The Cayley–Hamilton Theorems of Hypermatrix. These properties justify the reasonability of U-engenvalues/eigenvectors.
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Cheng et al. (2026) studied this question.
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