Introduction to Mathematical Logic, Sixth Edition
《Introduction to Mathematical Logic, Sixth Edition》 · 第 48 页 · Chapter 1，Section 1.5.3
We set $\mathcal E^\rho = \{f_B^\rho : B \in \operatorname{End}(V)\}$. This is the linear subspace of $\mathcal O[G]$ spanned by the functions in the matrix for $\rho$. It is finite-dimensional and invariant under left and right translations by $G$. We call it the space of representative functions associated with $\rho$.