---
date: 2022-04-05 23:42
modification date: Thursday 26th May 2022 16:59:15
title: "characters"
aliases: [character]
---

Last modified date: <%+ tp.file.last_modified_date() %>

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

---

# characters

A character of a representation $\phi: G\to V$ is defined as 
$$
\chi_\phi(g) := \Tr(\phi(g))
,$$
i.e. by taking the trace of the image of $g$ in any basis.

Big result:
An irreducible representation of a finite group $G$ is completely determined by its character.

![](attachments/Pasted%20image%2020220526165922.png)