Mathematics Asked by Abdul Fatir on December 30, 2020

Let $f:mathbb{R}^m to mathbb{R}^n: x to f(x)$ be a continuous and differentiable function with $m < n$. If the Jacobian $J_f$ has full column rank (i.e., rank=$m$) $forall x in mathbb{R}^m$, does this imply that $f$ is an injective function? If yes, can I get a reference for this result?

No, take $f(t) =pmatrix{ sin t\ cos t}$.

Correct answer by daw on December 30, 2020

Get help from others!

Recent Answers

- haakon.io on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- Jon Church on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?

Recent Questions

- How can I transform graph image into a tikzpicture LaTeX code?
- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP