Let $M _ { n } ( \mathbb { C } )$ denote the set of $n \times n$ matrices over $\mathbb { C }$. Think of $M _ { n } ( \mathbb { C } )$ as the $2 n ^ { 2 }$-dimensional Euclidean space $\mathbb { R } ^ { 2 n ^ { 2 } }$. Show that the set of all diagonalizable $n \times n$ matrices is dense in $M _ { n } ( \mathbb { C } )$.