# Some results of strongly primitive tensors

## TL;DR

This paper characterizes strongly primitive tensors of order m and dimension 2, relates their properties to majorization matrices, and explores properties for higher dimensions, proposing future research directions.

## Contribution

It provides a complete characterization of strongly primitive tensors of order m and dimension 2, linking their primitiveness to that of their majorization matrices.

## Key findings

- Order m dimension 2 tensor is primitive iff its majorization matrix is primitive
- Characterization of strongly primitive tensors of order m and dimension 2
- Proposed open problems for tensors with dimension n ≥ 3

## Abstract

In this paper, we show that an order $m$ dimension 2 tensor is primitive if and only if its majorization matrix is primitive, and then we obtain the characterization of order $m$ dimension 2 strongly primitive tensors and the bound of the strongly primitive degree. Furthermore, we study the properties of strongly primitive tensors with $n\geq 3$, and propose some problems for further research.