Weyl's unitary trick

This article gives the statement, and possibly proof, of a basic fact in linear representation theory.
View a complete list of basic facts in linear representation theory OR View all facts related to linear representation theory

Statement

For finite groups

If $V$ is a complex linear representation of a finite group $G$ then $V$ has a $G$-invariant inner product.

For compact groups

If $G$ is a compact group, then every complex representation of $G$ is unitary.

Proof

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