A surjective linear map is any linear map which satisfies the surjective property. This property has a few consequences for the matrix which represents the map.

For a map represented by a matrix such that the following properties are all equivalent

1. is a surjective linear map
2. has at least one solution for every in
3. is consistent for every in
4. The columns of span
5. has a pivot in every row.
6. The range of has dimension