TITLE: Why is the determinant $M_n(\mathbb R) \to \mathbb R$ continuous?
QUESTION [46 upvotes]: Why is the determinant as a function from $M_n(\mathbb{R})$ to $\mathbb{R}$ continuous, please can anyone explain precisely and rigorously? So far I know the explanation which comes from the facts: polynomials are continuous, sum and product of continuous functions are continuous. Also I have the confusion regarding the metric on $M_n(\mathbb{R})$

REPLY [5 votes]: It's continuous because it's computable as a function from $\mathbb{R}^{n^2}$ to $\mathbb{R}$.