define by

suppose is a linear map. let be a vector with in the th row and everywhere else. note that every can be written (uniquely) as where

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.

let then since is linear, we have: