Formalizing a Linear Algebra Proof with Lean

This article details the author's experience formalizing a simple theorem about the linear independence of eigenvectors in linear algebra using the Lean proof assistant. The article explains Lean's syntax, the use of the Mathlib library, and how automation tools simplify the proving process. The authors explore improving and generalizing the theorem and introduce Mathlib's version control and community collaboration. Finally, the article looks ahead to the role of proof assistants and AI in future mathematical research.