


An m x n matrix A defines a function T from R^{n} to R^{m} by taking a vector x in R^{n} to the vector T(x) = Ax in R^{m}.
A matrix map, such as T or S defined above, is a special case of a more general type of map called a linear transformation. A linear transformation from a vector space V to a vector space W is a function with domain V and target W that satisfies preserves the properties of addition and scalar multiplication. More precisely, a function T: V > W is a linear transformation provided that, for all vectors u and v in V and for all scalars c, the following two properties hold:
then
Show that T is a linear transformation.



modules at math.duke.edu  Copyright CCP and the author(s), 1999 