# Expression of a Real Matrix as a Difference of a Matrix and its Transpose Inverse

## TL;DR

This paper presents a novel way to express any real matrix as the difference between a matrix and the transpose of its inverse, potentially aiding control theory and matrix analysis applications.

## Contribution

It introduces a new representation of real matrices as a difference involving transpose-inverse terms, addressing existing obstacles in control and computational applications.

## Key findings

- Provides a general formula for the representation
- Facilitates analysis in control theory
- Potentially simplifies matrix computations

## Abstract

In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of transpose-inverse terms prove to be obstacles, particularly in control theory and related applications such as computational simulation and analysis of matrix representations of articulated figures.