- #1

- 3,507

- 26

Is an injective endomorfism automatically bijective?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter TrickyDicky
- Start date

- #1

- 3,507

- 26

Is an injective endomorfism automatically bijective?

- #2

- 341

- 51

- #3

- 3,507

- 26

finite-dimensional spaces, then yes. This is known as the Fredholm alternative: http://en.wikipedia.org/wiki/Fredholm_alternative

Thanks for confirming that intuition and for the pointer to Fredholm alternative, never heard of it.

- #4

WWGD

Science Advisor

Gold Member

- 5,489

- 3,948

Doesn't this follow from rank-nullity theorem?

- #5

mathwonk

Science Advisor

Homework Helper

2020 Award

- 11,137

- 1,330

- #6

- 341

- 51

Doesn't this follow from rank-nullity theorem?

Yes. But the Fredholm alternative also hold in some infinite-dimensional cases. There, you can't use rank-nullity.

Share:

- Last Post

- Replies
- 7

- Views
- 979