It seems that there’s a loose way of discussing group representations that’s fine for the initiated, but confusing for the neophyte: I understand that the objects that represent group operations are usually (or always?) square matrices, which naturally can be described as “matrix representations” (of the group operations). In which case, what exactly (in natural language) is something described as e.g. “a spinor rep” or “a tensor rep”? Does that mean: - The matrix representation of a group (symmetry) operation acting ON something that is a spinor, or (…whatever)? OR - A group operation REPRESENTED BY a spinor (i.e. the representation of a group (symmetry) operation is itself a spinor? (But then, acting on what?)) What confuses this slightly more is that a spinor can itself be expressed as a square matrix, as can a tensor, so it looks like it is possible for a matrix representation of an operation to also be itself a spinor or tensor? Can this be so? Could some natural-language-capable person please clarify. Thank you.