Let L: -> be a linear operator. If A is the standard matrix representation of L, then an nxn matrix B is also a matrix representation of L.
I understand that if an operator goes from two spaces that are equal (As in this case, with 2-d going to 2-d), then a matrix representation A such that L(x) = Ax for any x in R^n must be nxn. But how do I know if all nxn matrices can be standard matrix representations?
This is the way the question was written, btw.