2017/12/12 by Alexander Gamkrelidze, Gamkrelidze, Alexander, G. Giorgadze +1
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #History and Overview (math.HO) #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1712.04244
openalex publication_date 2017/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this Note we show that the notion of a basis of a finite-dimensional vector space could be introduced by an argument much weaker than Gauss' reduction method. Our aim is to give a short proof of a simply formulated lemma, which in fact is equivalent to the theorem on frame extension, using only a simple notion of the kernel of a linear mapping, without any reference to special results, and derive the notions of basis and dimension in a quite intuitive and logically appropriate way, as well as obtain their basic properties, including a lucid proof of Steinitz's theorem.