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