- #36

etotheipi

Mark44 said:But here (-1) is shorthand for ##-1 \cdot (-\pi)##, so every representation of an element in the vector space ##\mathbb R## by its coordinate is implicitly in terms of the basis, ##-\pi##. That's been my point all along in this thread.

I think the point is that ##[-\pi]_{\beta} = (-1)##, that is the mapping to the coordinate vector w.r.t. ##\beta##. But the actual element of ##V## is ##-\pi##, a 1-tuple. The tuple itself, ##(-\pi)##, is not written in any basis, because it

*is*the vector.