# Core and Core-EP Inverses of Tensors

## TL;DR

This paper introduces new definitions and properties of core and core-EP inverses for complex tensors, providing novel algebraic characterizations and representations that extend existing matrix concepts.

## Contribution

It presents the first algebraic approach to defining and analyzing core and core-EP inverses for tensors, expanding the theoretical framework beyond matrices.

## Key findings

- New definitions of core and core-EP inverses for tensors
- Characterizations and properties of these inverses
- Verification of results using a novel algebraic approach

## Abstract

Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific algebraic approach, based on proposed definitions and previously verified properties. The approach used here is new even in the matrix case.