Degree of a linear representation

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 $$(V,\rho)$$ is a linear representation of a group $$G$$ over a field $$k$$, i.e. we have a homomorphism $$\rho:G \to GL(V)$$, where $$V$$ is a vector space over $$k$$. Then, the degree of the representation $$(V,\rho)$$ is defined as the dimension of $$V$$ as a $$k$$-vector space.

For a finite group, the degrees of irreducible representations are important numbers.