# Thread: A linear which is not injective?

1. ## A linear which is not injective?

Hi,

exist a special case, where we have a map which is completly linear that is not injective?

greetings

p.s.

I heard that injective in english is also translated to "one-to-one" Is this correct?

2. Hi.
What do you mean by completely linear?

3. That there is no power higher than one.

greetings

4. The zero map is a linear map, and it is not injective!

In the particular case of linear maps from $\mathbb{R}$ to $\mathbb{R}$, a linear map is injective (and even bijective) iff it is a non constant map.

In a more general case, linear map between two vector spaces can be non injective without being a constant map, for exemple
$f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}x,y)\mapsto (x+y,0)" alt="f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}x,y)\mapsto (x+y,0)" />

p.s. Yes, one-to-one means injective.