Let T,S : V → W be two linear transformations, and suppose B1 = {v1,...,vn} andB2...

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 Matm×n(F) are isomorphic. (Hint: the function MB1,B2 : L(V,W) → Matm×n(F) is linear by (a) and (b). Show that it is a bijection. A linear transformation is uniquely specified by its action on a basis.)

need clearly proof

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Colby Messinger answered 10 months ago

Let W be an inner product space and v1, . . . , vn a basis...

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Let T,S : V → W be two linear transformations, and suppose B1 = {v1,...,vn} andB2...

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