Subspace
A subset of that is a vector space under the operations of ; equivalently, for all .
Criterion and trivial subspaces
A subset is a subspace precisely when it is non-empty and for all and scalars . In particular, is always a subspace of . The two trivial subspaces of any vector space are and itself.
Related
Stated in
- Definition 2.49 (Subspace)§2.10 General Vector Spaces