= Normalized convolution on a finite group
{title2=$(f*g)(x)=\mathbb E_yf(y)g(y^{-1}x)$}
For scalar functions on a <finite group>, <normalized convolution on a finite group> is $(f*g)(x)=|G|^{-1}\sum_y f(y)g(y^{-1}x)$. It is associative and need not commute. Its identity is $|G|1_{\{e\}}$, rather than the unscaled <indicator function> of the identity element. The <Fourier analysis on a finite group> convention $\widehat f(\rho)=\mathbb E f(x)\rho(x)$ turns it into matrix multiplication in the same order.
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