Completely reducible linear representation

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.

Relation with other properties

Stronger properties

• Irreducible linear representation
• Isotypical linear representation