fill in the blanks here:

choose a basis for V and then find the ____ for a linear transformation. then find a basis for the set of _x_ _____s.

to pull this back to the set of all linear transformations, use the linear mapping corresponding to each basis ______ ,

which will be a basis for the set of all linear transformations V-->V.

(note: this only works for finite-dimensional vector spaces)

another, more direct approach: choose a basis {v1,v2,....,vn,....} for V (which may be finite, or infinite).

show that the set {Tij} where Tij(vk) = δjkvi, (where δjk is the kroenecker delta, δjj = 1, δjk = 0 j ≠ k) is a basis for the set of all linear maps V-->V.