On Linear Maps and Seed Sets of Beidleman Near-Vector Spaces

TL;DR

This paper investigates linear maps in Beidleman near-vector spaces, focusing on matrix representations and algorithms for seed set determination, advancing understanding of their algebraic structure and computational aspects.

Contribution

It introduces new methods for representing linear maps and algorithms for finding seed sets in finite-dimensional Beidleman near-vector spaces.

Findings

Matrix representations of linear maps are characterized.

Algorithms for seed set determination are developed.

Enhanced understanding of algebraic structure of Beidleman near-vector spaces.

Abstract

We studied linear mappings in Beidleman near-vector spaces and explored their matrix representations using $R$-bases of $R$-subgroups. Additionally, we developed algorithms for determining the seed number and seed sets of $R$-subgroups within finite-dimensional Beidleman near-vector spaces.