# Thread: Show set of linear transformations from R^n to R^m

1. ## Show set of linear transformations from R^n to R^m

Show that the set of all possible linear transformations from $\Re^n to \Re^m$, with addition and multiplication by a scalar defined by $(T_1 + T_2)(x) = T_1(x) + T_2(x)$ and $kT(x) = T(kx)$, is itself a vector space

2. Linear Algebra: A modern Introduction by David Poole gives those in his examples, a good book to check out!