Nonsingular derivative

  • #1
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?"
 

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
2,015
4
It probably means it's invertible (i.e. it's a bijection).
 
  • #3
998
0
What does the derivative of a function [itex]f:\mathbb{R}^n \rightarrow \mathbb{R}^m[/itex] look like? Do you know what it means for a matrix to be nonsingular (hint: see morphism's post!)? :smile:
 

Related Threads on Nonsingular derivative

  • Last Post
Replies
9
Views
1K
Replies
5
Views
20K
Replies
5
Views
4K
Replies
2
Views
1K
Replies
4
Views
2K
Replies
3
Views
1K
  • Last Post
Replies
1
Views
782
  • Last Post
Replies
7
Views
4K
Replies
7
Views
5K
Replies
6
Views
3K
Top