On the existence of vectors dual to a set of linear functionals

TL;DR

This paper provides a straightforward proof of a key lemma related to the existence of vectors dual to a set of linear functionals, which is fundamental in linear algebra and functional analysis.

Contribution

It offers a simple, inductive proof of a crucial lemma that was previously established through more complex methods.

Findings

Simplified proof of the lemma enhances understanding.

Clarifies the conditions for the existence of dual vectors.

Facilitates further research in linear functional analysis.

Abstract

We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].