On a characterization of finite-dimensional vector spaces
Marat V. Markin
TL;DR
This paper characterizes finite-dimensional vector spaces by examining the right-sided invertibility of linear operators acting on them, offering a new perspective on their structure.
Contribution
It introduces a novel characterization of finite-dimensionality based on the invertibility properties of linear operators.
Findings
Finite-dimensional vector spaces are characterized by right-sided invertibility of linear operators.
Provides a new criterion for finite-dimensionality in linear algebra.
Enhances understanding of the structure of vector spaces through operator invertibility.
Abstract
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
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