The Fourier transform of a function f : G \rightarrow \mathbb{C}\, at a representation \varrho : G \rightarrow GL(d_\varrho, \mathbb{C})\, of G\, is .
For each representation \varrho\, of G\,, \widehat{f}(\varrho)\, is a d_\varrho \times d_\varrho\, matrix, where d_\varrho\, is the degree of \varrho\,.