# Equality in the Matrix Entropy-Power Inequality and Blind Separation of Real and Complex sources

## TL;DR

This paper proves a matrix version of the entropy-power inequality for real and complex variables using a transportation argument, and applies it to blind source extraction.

## Contribution

It introduces a new matrix form of the entropy-power inequality and demonstrates its use in blind source separation.

## Key findings

- Established the matrix entropy-power inequality for real and complex cases.
- Provided a transportation-based proof that clarifies the equality conditions.
- Applied the inequality to improve blind source extraction techniques.

## Abstract

The matrix version of the entropy-power inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.