Corollary
Dimension Formula
For a finite group $G$ over $\mathbb{C}$, combining Maschke's Theorem and
Remark,
\[
\sum_{\chi \in \hat{G}} (\dim V_\chi)^2 = |G|.
\]
Used in
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
n692f1650["Maschke's Theorem for Compact Groups"]
nb96526a2["Remark"]
n3b157f10["Dimension Formula"]:::current
n1b852777["Character Table of $S_3$"]
n692f1650 --> n3b157f10
nb96526a2 --> n3b157f10
n3b157f10 --> n1b852777
click n692f1650 "../objects/692f1650.html" "_self"
click nb96526a2 "../objects/b96526a2.html" "_self"
click n1b852777 "../objects/1b852777.html" "_self"