Faithful linear representation

This article gives a basic definition in the following area: linear representation theory
View other basic definitions in linear representation theory |View terms related to linear representation theory |View facts related to linear representation theory

This article describes a notion of representation, or a group action on a certain kind of object.
View a complete list of types of representations

Definition

A linear representation is said to be faithful if, equivalently:

It has a trivial kernel.
It is injective.

Proof: Since linear representations are group homomorphisms, these conditions are equivalent by Group homomorphism injective iff trivial kernel.