An Explicit SOS Decomposition of A Fourth Order Four Dimensional Hankel Tensor with A Symmetric Generating Vector

TL;DR

This paper provides an explicit sum-of-squares (SOS) decomposition for a specific class of fourth-order, four-dimensional Hankel tensors with symmetric generating vectors at critical values, enhancing understanding of their positive semidefinite properties.

Contribution

It offers a new explicit SOS decomposition for a particular Hankel tensor class at critical points, supplementing existing theoretical results.

Findings

Explicit SOS decomposition constructed at critical value.

Advances understanding of positive semidefinite Hankel tensors.

Supports theoretical analysis with concrete decomposition examples.

Abstract

In this note, we construct explicit SOS decomposition of A Fourth Order Four Dimensional Hankel Tensor with A Symmetric Generating Vector, at the critical value. This is a supplementary note to Paper [3].