# Degree of a linear representation

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

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## Definition

### Symbol-free definition

The degree of a linear representation is defined as the dimension of the vector space to which the representation's map is defined.

It also equals the value of the character at the identity element.

### Definition with symbols

Suppose is a linear representation of a group over a field , i.e. we have a homomorphism , where is a vector space over . Then, the degree of the representation is defined as the dimension of as a -vector space.

For a finite group, the degrees of irreducible representations are important numbers. `Further information: degrees of irreducible representations`