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