Miguel Mitrofanov
Grrr...must...hold...my...tongue...
Dan, as a former student of a clone of that physics teacher, I am really interested in what you will say when you fail to hold your tongue.
-- Bill Wood
MV> I have to admit I was wondering the same thing myself.
So was I.
I'm guessing that Dan means that thinking of tensors as things that transform between co-ordinate systems in a certain way (e.g. via the Jacobian of the transition maps) isn't a terribly good way of thinking about them. Vector fields, co-vector fields and tensor fields are really co-ordinate independent notions and the transformation laws (if I may call them that) are a consequence of the way they transform under (smooth) maps. But perhaps this is better discussed on a differential geometry mailing list? Dominic.