Abstract
In this paper, we propose a definition for eigenvalues of odd-order tensors based on some operators. Also, we define the Schur form and the Jordan canonical form of such tensors, and discuss commuting families of tensors. Furthermore, we prove some eigenvalue inequalities for Hermitian tensors. Finally, we introduce characteristic polynomials of odd-order tensors.
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Pakmanesh, M., Afshin, H. \(T_M\)-Eigenvalues of Odd-Order Tensors. Commun. Appl. Math. Comput. 4, 1258–1279 (2022). https://doi.org/10.1007/s42967-021-00172-z
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DOI: https://doi.org/10.1007/s42967-021-00172-z
Keywords
- \(T_M\)-product
- \(T_M\)-eigenvalue
- \(T_M\)-Schur form
- \(T_M\)-Jordan canonical form
- Odd-order tensor
- \(F_M\)-upper (lower) triangular tensor