Rank of 3-tensors with 2 slices and Kronecker canonical forms

TL;DR

This paper investigates the rank of 3-tensors with 2 slices, focusing on conditions for diagonalizability when adding such tensors to a given tensor over complex and real fields.

Contribution

It provides a method to determine the tensor rank ensuring diagonalizability of the sum with a given 3-tensor with 2 slices.

Findings

Derived conditions for diagonalizability of tensor sums

Established rank bounds for 3-tensors with 2 slices

Analyzed tensor properties over complex and real fields

Abstract

Tensor type data are becoming important recently in various application fields. We determine a rank of a tensor T so that A+T is diagonalizable for a given 3-tensor A with 2 slices over the complex and real number field.