Positive definiteness of fourth order three dimensional symmetric tensors

2024/06/06 by Yisheng Song, Song, Yisheng
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC) #Structural Analysis and Optimization #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2406.04010

openalex publication_date 2024/06/06 · openalex created_date 2024/06/08 · openalex updated_date 2026/07/28

Abstract

For a 4th order 3-dimensional symmetric tensor with its some entries 1 or -1, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for ternary quartic homogeneous polynomials.

Related

• Positive definiteness of a class of cyclic symmetric tensors
• Copositivity criteria of a class of fourth order 3-dimensional symmetric tensors
• Positive Definiteness of 4th Order 3-Dimensional Symmetric Tensors with entries -1, 0, 1
• The analytic criterion of strict copositivity for a 4th-order 3-dimensional tensor
• Strict Copositivity for a Class of 3rd Order Symmetric Tensors