Subspace.md (558B)
1 # Subspace 2 3 **Source:** Linear Algebra Done Right 4 5 **Chapter:** 1 6 7 ### Linear Algebra Context 8 9 **Definition:** A subspace is a subset of a vector space. 10 11 To verify a subset U of a vector space V is a subspace of V we only need to verify: 12 13 1. Closed under addition 14 2. Closed under scalar multiplication 15 3. Additive Identity 16 17 ### ML Context 18 19 **Definition:** A subspace is a lower dimensional space. 20 21 Often we find that many higher dimensional points all reside in or near a similar lower dimensional subspace which is the basis for [Projection](Projection.md)