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.
Related pages[change | change source]
References[change | change source]
- Axler, Sheldon (2015). Linear Algebra Done Right (Third ed.). Springer International Publishing. p. 18. doi:10.1007/978-3-319-11080-6. ISBN 978-3-319-11079-0.
- "Subspace | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-08-23.
- "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-23.
- "4.4: Sums and direct sum". Mathematics LibreTexts. 2013-11-07. Retrieved 2020-08-23.