---
tag: 5FW1MD0HNV
kind: concept
name: Faithful representation
sources:
  - wikipedia: en:2617872@r1343245842
    locator: Faithful representation
    note: adopted
    mention: wikipedia://en/2617872
    sections: [Summary]
same_as:
  wikidata: Q5431294
  wikipedia: Faithful representation
inventory: [DZHK3M9EQ8]
---

## Summary

In mathematics, especially in an area of abstract algebra known as representation theory, a **faithful representation** ρ of a group $G$ on a [[vector space|000AYPA9AJ]] $V$ is a linear representation in which different elements $g$ of $G$ are represented by distinct linear mappings $\rho(g)$. In more abstract language, this means that the [[group homomorphism|0HV9Y7WG5R]] $\rho: G\to GL(V)$ is injective (or one-to-one).