On the real rank of monomials

TL;DR

This paper investigates the real rank of monomials, providing an upper bound and characterizing when real and complex ranks coincide, enhancing understanding of tensor decompositions in algebraic geometry.

Contribution

It introduces an upper bound for the real rank of monomials and characterizes the conditions under which real and complex ranks are equal.

Findings

Real and complex ranks of monomials coincide iff the least exponent is one.

An explicit upper bound for the real rank of all monomials is established.

The paper advances the understanding of monomial tensor decompositions.

Abstract

In this paper we study the real rank of monomials and we give an upper bound for the real rank of all monomials. We show that the real and the complex ranks of a monomial coincide if and only if the least exponent is equal to one.