- #1
NoOne0507
- 16
- 0
If V is a vectorspace and v is a vector in V. will the projection of v onto V be v?
Is a vector in a vectorspace its own projection onto that vectorspace?
- Thread starter NoOne0507
- Start date
-
- Tags
- Projection Vector
In summary, a vector space is a mathematical structure that consists of a set of vectors that can be added and multiplied by scalars. A projection onto a vector space is a way of mapping a vector onto a subspace of that vector space. Yes, a vector can be its own projection onto a vector space, which happens when the vector is already in the subspace onto which it is being projected. If a vector is its own projection, it means that it is already in the subspace, making calculations and understanding the properties of the vector space easier. To determine if a vector is its own projection, you can compare it to the basis vectors of the subspace and see if it is a linear combination of those vectors.
- #2
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
Hi NoOne0507! 
If you mean "if V is a subspace of vectorspace W and v is a vector in V will the projection of v onto V be v?", the answer is, yes.
If you mean "if V is a subspace of vectorspace W and v is a vector in V will the projection of v onto V be v?", the answer is, yes.