A linear map L: R^n -> R is linear for all v, w that exist in R^n and all a, b that exist in R if...

L(av + bw) = aL(v) + bL(w)

Show that for any vector u that exists in R^n, the transposed vector u^T represents a linear map of type R^n -> R

Also, prove conversely that a linear map L:R^n -> R can be represented as the transpose u^T of a vector u that exists in R^n.

Sorry for the lack of latex usage. I don't know all the symbols and I'm hoping for an answer as soon as possible.

Thanks for your help.

Sean.