Vector subspace facts for kids
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
See also
In Spanish: Subespacio vectorial para niños
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Vector subspace Facts for Kids. Kiddle Encyclopedia.