Subspaces

Subspaces are a type of Subset following special rules. A subset is a subspace if:

  • contains the all-zero vector
  • is closed under addition. That is, if and then .
  • is closed under scalar multiplication. That is, if and , then .

Subspaces of :

  • Line through the origin
  • Origin

Subspaces of :

  • Origin
  • Line through origin
  • Plane through origin