Positive definiteness of a class of cyclic symmetric tensors
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929484110757888 |
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| author | Song, Yisheng |
| author_facet | Song, Yisheng |
| contents | For a 4th order 3-dimensional cyclic symmetric tensor, a sufficient and necessary condition is bulit for its positive semi-definiteness. A sufficient and necessary condition of positive definiteness is showed for a 4th order $n$-dimensional symmetric tensor. With the help of such a condition, the positive definiteness of a class of 4th order 3-dimensional cyclic symmetric tensors is given. Moreover, the positive definiteness of a class of non-cyclic symmetric tensors is showed also. By applying these conclusions, several (strict) inequalities are erected for ternary quartic homogeneous polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive definiteness of a class of cyclic symmetric tensors Song, Yisheng Optimization and Control Algebraic Geometry For a 4th order 3-dimensional cyclic symmetric tensor, a sufficient and necessary condition is bulit for its positive semi-definiteness. A sufficient and necessary condition of positive definiteness is showed for a 4th order $n$-dimensional symmetric tensor. With the help of such a condition, the positive definiteness of a class of 4th order 3-dimensional cyclic symmetric tensors is given. Moreover, the positive definiteness of a class of non-cyclic symmetric tensors is showed also. By applying these conclusions, several (strict) inequalities are erected for ternary quartic homogeneous polynomials. |
| title | Positive definiteness of a class of cyclic symmetric tensors |
| topic | Optimization and Control Algebraic Geometry |
| url | https://arxiv.org/abs/2409.01747 |