Have you tried doing any calculations at all? Whatis" R≤3[x] "? What do derivatives of those functions look like?

If you tried the simpler example, derivative operator on linear functions, any such function would be of the form y= ax+ b and its derivative would be dy/dx= a. A standard basis would be and so that and the derivative would be . Using that basis, the matrix representation would be . Can that be diagonalized or orthogonalized.