Vector Subspace

Last updated Nov 1, 2022

Suppose $V$ is a Vector Space over Field $F$. Supppose $W \subset V$ and $W$ is a Vector Space over $F$ when endowed with the same $+$ and $*$ operations as $V$. Then we say $W$ is a Vector Subspace of $V$.

1. A Subset of a Vector Space is a Subspace iff it is closed under scaling and addition
2. Intersection of Vector Subspaces is a Vector Subspace
3. Finite Sum of Vector Subspaces is a Vector Subspace

1. Space of Polynomials over a Field form a Vector Subspace of Function Vector Space Consider