# A note on the surjectivity of operators on vector bundles over discrete spaces

## TL;DR

This paper provides a concise proof of a criterion for solvability of linear equations in infinite variables and applies it to analyze the surjectivity of magnetic Schrödinger operators on bundles over graphs.

## Contribution

It introduces a simplified proof of Eidelheit's criterion and applies it to the study of operator surjectivity on discrete space bundles.

## Key findings

- Established a criterion for solvability in infinite-dimensional linear equations.
- Applied the criterion to magnetic Schrödinger operators on graph bundles.
- Provided conditions for operator surjectivity in discrete settings.

## Abstract

In this note we give a short and self-contained proof for a criterion of Eidelheit on the solvability of linear equations in infinitely many variables. We use this criterion to study the surjectivity of magnetic Schr\"odinger operators on bundles over graphs.