Linear mapping/Image and preimage/Linear subspaces/Fact
Let be a field, let and denote -vector spaces and let
be a -linear mapping. Then the following hold.
- For a linear subspace , the image is a linear subspace of .
- In particular, the image of the mapping is a linear subspace of .
- For a linear subspace , the preimage is a linear subspace of .
- In particular, is a linear subspace of .