# Multilinear mappings versus homogeneous polynomials and a multipolynomial polarization formula

## TL;DR

This paper demonstrates that (k,m)-linear mappings are special cases of polynomials, reveals overlooked properties such as all multilinear mappings being homogeneous polynomials, and offers new polarization formulas.

## Contribution

It establishes the connection between multilinear mappings and polynomials and introduces new polarization formulas, clarifying previously overlooked properties.

## Key findings

- Every multilinear mapping is a homogeneous polynomial
- (k,m)-linear mappings are particular cases of polynomials
- New polarization formulas are provided

## Abstract

We show that (k,m)-linear mappings, introduced by I. Chernega and A. Zagorodnyuk in [3], are particular cases of polynomials. As corollaries, we expose some apparently overlooked properties in the literature. For instance, every multilinear mapping is a homogeneous polynomial. Contributions to the polarization formula are also provided.