# Completely reducible linear representation

From Groupprops

*This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field*

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

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## Definition

### Symbol-free definition

A linear representation of a group is said to be **completely reducible** if it can be expressed as a direct sum of irreducible linear representations.