Orthogonal representation

This article provides a semi-basic definition in the following area: linear representation theory

Definition

Let $G$ be a group and $k$ a field. An orthogonal representation of $G$ over $k$ is a homomorphism $\rho :G\to O(n,k)$ where $O(n,k)$ is the orthogonal group of order $n$ over the field <amth>k</math> (for some finite $n$).

Since $O(n,k)$ is a subgroup of $GL(n,k)$, every orthogonal representation can be viewed as a linear representation.