# A linear map is injective if and only if its kernel is trivial

From Maths

This page is a

*dire page*and is in desperate need of an update.## Notes

See

- Notes:Advanced_Linear_Algebra_-_Roman/Chapter_2#Theorem_2.3:_equivalent_statements_to_a_linear_map_being_surjective_.2F_injective
- A linear map is injective if and only if the image of every non-zero vector is a non-zero vector

Some redirects are needed and whatnot.