# Character of a linear representation

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*This term makes sense in the context of a linear representation of a group, viz an action of the group as linear automorphisms of a vector space*

This article gives a basic definition in the following area: linear representation theory

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## Definition

### Definition in terms of linear representation as a homomorphism

Let be a group and be a finite-dimensional linear representation over a field . Then, the character of is the composite where is the trace map from to .