Orthogonal representation
= Orthogonal representation
An <orthogonal representation> is a real <group representation> preserving a positive-definite <inner product>, equivalently a <group homomorphism> into an <orthogonal group>. Every finite-dimensional <continuous> <real representation> of a <compact group> has this form after averaging an <inner product> over <Haar measure>, by <orthogonalization of a compact-group representation>.