# Nonsingular derivative

1. Apr 11, 2007

### JamesTheBond

What does a "nonsingular derivative" mean. It comes in the following context: "If f: R^2 --> R^2 is a function with a nonsingular derivative everywhere, is f bijective?"

2. Apr 11, 2007

### morphism

It probably means it's invertible (i.e. it's a bijection).

3. Apr 11, 2007

### Data

What does the derivative of a function $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$ look like? Do you know what it means for a matrix to be nonsingular (hint: see morphism's post!)?