Within spaces ( **subspaces**.

To give na example, a subspace of

- The set includes the zero vector
- The set is closed under scalar multiplication
- The set is closed under addition

Keep in mind that the first condition, that

a subspace must include the zero vector, is logically already included as part of the second condition, thata subspace is closed under multiplication.

A span is always a subspace.

Тhe zero vector is always a subspace.

Аn entire space