Geodesic
The maximum and minimum value of homogeneous polynomial under different norms via tensors
Filomat, Tome 37 (2023) no. 16, p. 5361

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DOI

For any homogeneous polynomial, it can be expressed as the product of a tensor A and a vector x, we denote it by P A (x). With the change of the norm of x, the maximum value (resp. the minimum value) of P A (x) is changed. In this paper, by the properties of tensor A, we study the relationships between the maximum values (resp. minimum values) of P A (x) under different norms of x. We present that the maximum values (resp. the minimum values) of P A (x) at different norms of x always have the same sign. Moreover, the relationship between the magnitudes of the maximum values (resp. the minimum values) of P A (x) at different norms of x are characterized. Further, some inequalities on H-eigenvalues and Z-eigenvalues of tensor A are obtained directly. And some applications on definite positive of tensors and hypergraphs are given.
DOI : 10.2298/FIL2316361D
Classification : 15A69, 15A18
Keywords: Homogeneous polynomial, Tensor, H(Z)-eigenvalue, Spectral radius 
Chunli Deng; Haifeng Li; Changjiang Bu. The maximum and minimum value of homogeneous polynomial under different norms via tensors. Filomat, Tome 37 (2023) no. 16, p. 5361 . doi: 10.2298/FIL2316361D
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     title = {The maximum and minimum value of homogeneous polynomial under different norms via tensors},
     journal = {Filomat},
     pages = {5361 },
     year = {2023},
     volume = {37},
     number = {16},
     doi = {10.2298/FIL2316361D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2316361D/}
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