Let be a
field
and let be a
-vector space. Then the following hold.
- Let
, ,
be a family of subspaces of . Then the intersection
-
is a linear subspace.
- Let
, ,
be a family of elements of and consider the subset of which is given by all linear combinations of these elements. Then is a linear subspace of .
- The family , ,
is a system of generators of if and only if
-