Wronskians and linear independence

TL;DR

This paper presents a new, simplified proof demonstrating that a finite set of analytic functions has a zero Wronskian only when the functions are linearly dependent, clarifying a fundamental concept in analysis.

Contribution

It provides a novel, straightforward proof of the relationship between zero Wronskian and linear dependence for analytic functions.

Findings

Zero Wronskian implies linear dependence for finite analytic functions

Simplified proof enhances understanding of Wronskian properties

Clarifies fundamental relationship in analysis

Abstract

We give a new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent.