Could you give an example, a little more info on how this was explained to you?

I think you're talking about polynomial spaces in the "power" basis, where the basis is {1, x, x^2, ... }.

You will have a vector that represents a polynomial in the "power" basis (other bases do exist, of course, and some may actually be better than the power basis for solving this problem, but I assume that's what you're using), and your idea is to multiply it by a matrix and produce another vector that will represent the derivative of the original polynomial.

If that's not what you're trying to do, let me know.