Positive Definiteness of a Class of Cyclic Symmetric Tensors

Yisheng Song ()
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Yisheng Song: Chongqing Normal University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 14, 19 pages

Abstract: Abstract For a fourth order three-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 fourth order n-dimensional symmetric tensor. With the help of such a condition, the positive definiteness of a class of fourth order three-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.

Keywords: Positive semi-definiteness; Cyclic symmetric; Ternary quartic; 90C23; 15A69 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02615-6

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