Representation Theory: Irreducible Characters Are an Orthonormal Basis @MuPrimeMath

Uploaded September 2021 | Updated September 2026, 1 week ago

A key result in complex representation theory is the fact that, under a specific Hermitian inner product, the characters of the irreducible representations of a finite group G are an orthonormal basis for the vector space of complex-valued class functions on G. This video is an explanation and proof of why the irreducible characters are an orthonormal basis.

Ring & Module Theory playlist: youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7

0:00 Orthonormal
10:19 Basis
21:15 Summary

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Music: C418 - Pr Department

Representation Theory: Irreducible Characters Are an Orthonormal Basis

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