I'm learning about affine schemes and want to know if the functor $X : Alg_R \to Sets$ defined such that $$X(\mathbf{C}) = \{x \in M_{n \times n}(\mathbf{C}) | x \mbox{ has $n$ distinct eigenvalues}\}$$ where $M_{n \times n}(\mathbf{C})$ denotes the set of $n\times n$ matrices with entries in $C$, defines an affine functor.
Thus I'm trying to write it in the form $$X(\mathbf{C}) = \{ x \in \mathbf{C}^n | f(x)=0, \, \forall f \in T\}$$ where $T$ defines a set of polynomials on $\mathbf{C}^n$.
I think it should be possible but I can't seem to work out how I could possibly write it like that. Any help would be great!