Let V and W be vector spaces over F field, dimV=n, and dim W=m. What is the dimension of the vector space L(V,W), and what is an optional basis?

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- Dec 2nd 2011, 01:45 AMnorickaQuestion on linear transformaiton
Let V and W be vector spaces over F field, dimV=n, and dim W=m. What is the dimension of the vector space L(V,W), and what is an optional basis?

Thank you! - Dec 2nd 2011, 02:05 AMFernandoRevillaRe: Question on linear transformaiton
: If we fix $\displaystyle B_V$ and $\displaystyle B_W$ basis of $\displaystyle V$ and $\displaystyle W$ respectively, there is a natural isomorphism $\displaystyle \phi:\mathcal{L}(V,W)\to \mathbb{K}^{m \times n}$ given by $\displaystyle \phi (T)=[T]_{B_V}^{B_W}$ .__Hint__ - Dec 2nd 2011, 11:28 AMDevenoRe: Question on linear transformaiton
you may also wish to consider $\displaystyle E_{i,j} \in \mathcal{L}(V,W) : E_{i,j}(a_1v_1+a_2v_2+\dots+a_nv_n) = a_jw_i$.