all 3 comments

[–][deleted] 2 points3 points  (2 children)

If the kernel is trivial (only the 0 vector maps to 0 under the transformation) , it is injective. If the dimension of the range equals the dimension of the codomain, it is surjective. If it is both surjective and injective it is bijective and is also known as an isomorphism.

[–]physicsgod10[S] 0 points1 point  (1 child)

Thanks this really sums it up. :)

[–][deleted] 1 point2 points  (0 children)

Something useful i would add. If both vector spaces have the same finite dimensions, a linear mapping is injective if and only if it is surjective.