Let T,S : V ? W be two linear transformations, and suppose B1 =
{v1,...,vn} andB2...
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Let T,S : V ? W be two linear transformations, and suppose B1 ={v1,...,vn} andB2 = {w1,...,wm} are bases of V and W,respectively.
(c) Show that the vector spaces L(V,W) and MatmĂ—n(F) areisomorphic. (Hint: the function MB1,B2 : L(V,W) ? MatmĂ—n(F) islinear by (a) and (b). Show that it is a bijection. A lineartransformation is uniquely specified by its action on a basis.)
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