Diagonalizable

An operator T on a finite-dimensional vectorspace V is diagonalizeable if V has a basis of eigenvectors for T.

Denseness of diagonalizeable operators

The space of complex linear operators on <math>\mathbb{C}^n</math> may be identified with the vectorspace <math>M_n(\mathbb{C})</math> of nxn matrices with complex coefficients. As such, it inherits a natural structure as a topological space.

Given this topology, the set of diagonalizeable maps is a dense subset of <math>M_n(\mathbb{C}^n)</math>