# Preserving the trace of the Kronecker sum

## TL;DR

This paper investigates linear transformations that preserve the trace of Kronecker sums and explores their relationship with preservers of determinants of Kronecker products, highlighting the roles of partial trace and partial determinant.

## Contribution

It characterizes linear preservers of the trace of Kronecker sums and links them to preservers of determinants of Kronecker products using partial trace and partial determinant.

## Key findings

- Characterization of linear preservers of Kronecker sum trace
- Connection established between trace preservers and determinant preservers
- Role of partial trace and partial determinant in these preservers

## Abstract

The aim of this paper is to study linear preservers of the trace of Kronecker sums and their connection with preservers of determinants of Kronecker products. The partial trace and partial determinant play a fundamental role in characterizing the preservers of the trace of Kronecker sums and preservers of the determinant of Kronecker products respectively.