[ She pulls out a chair also, and lays the book open on the table. ]

The vector spaces over a linear field. Let us consider the transformations from one to another, say U and V over space K.

[ ... blah blah blah. Orianna speaks clinically and runs her fingers over the corresponding pieces of proof in her notebook. She has underlined in red things that she is unsure about, and hands Lux a pencil of her own so that she may write her own input. ]