Vector subspace

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.
If  and  are subspaces of a vector space , then the sum and the direct sum of  and , denoted respectively by  and , are subspaces as well.

 Related pages 
 Parallel projection

 References 

Category:Linear algebra