I would imagine that 19th century algebraists studying linear changes of
variable would have had occasion to think about maps like
(x,y)-->(ax+by,cx+dy),
as would the founders of multivariable calculus.
Does any particular mathematician, or small crowd of mathematicians, deserve
credit for focussing on the class of transformations of this kind, and for
the associated geometrical picture?
(I am asking the question for two dimensions because I am supposing that the
study of this situation preceded the study of analogous higher-dimensional
situations, though I can believe that this supposition might be wrong.)
Jim Propp
Department of Mathematics
University of Wisconsin