The English used in this article may not be easy for everybody to understand. (January 2012)
A vector subspace is a vector space that is a subset of another vector space. This means that all the properties of a vector space are satisfied. Let W be a non empty subset of a vector space V, then, W is a vector subspace if and only if the next 3 conditions are satisfied:
- additive identity – the element 0 is an element of W: 0 ∈ W
- closed under addition – if x and y are elements of W, then x + y is also in W: x, y ∈ W implies x + y ∈ W
- closed under scalar multiplication – if c is an element of a field K and x is in W, then cx is in W: c ∈ K and x ∈ W implies cx ∈ W.