Canonical Forms of $2 \times 2 \times 2$ and $2 \times 2 \times 2 \times 2$ Symmetric Tensors over Prime Fields

Stavros G. Stavrou

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arXiv · 1209.5021

Canonical Forms of $2 \times 2 \times 2$ and $2 \times 2 \times 2 \times 2$ Symmetric Tensors over Prime Fields

Stavros G. Stavrou

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Abstract

We consider symmetric tensors of format $2 \times 2 \times 2$ and $2 \times 2 \times 2 \times 2$ over prime fields. Using computer algebra we compute the canonical forms of these tensors. For $2 \times 2 \times 2$ symmetric tensors, we consider the prime fields $\mathbb{F}_p$ for $p = 2, 3, 5, 7, 11, 13, 17$. For $2 \times 2 \times 2 \times 2$ symmetric tensors, we consider the prime fields $\mathbb{F}_p$ for $p = 2, 3, 5, 7$. For each canonical form, we determine the size of its orbit and the symmetric rank of the symmetric tensors in its orbit.

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Stavros G. Stavrou. 2012-09-22. Canonical Forms of $2 \times 2 \times 2$ and $2 \times 2 \times 2 \times 2$ Symmetric Tensors over Prime Fields. https://arxiv.org/abs/1209.5021

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