- #1
Ghost of Progress
- 5
- 0
I want to project a vector from R3 onto a subspace.
I'll let the bases for the subspace be [a,b,c]T
(my T's mean transpose)
---
I have the defintion for vector projection
p = (<u,v>/<v,v>)*v
---
I know v will be the [a,b,c]T vector but what is u?
The only thing I could think of is let it be the triplet [x,y,z]T which could be any vector in R3.
---
Using this I get
p = [(a/(a^2 + b^2 + c^2))(ax + by + cz)]
[(b/(a^2 + b^2 + c^2))(ax + by + cz)]
[(c/(a^2 + b^2 + c^2))(ax + by + cz)]
---
I'm not very confident with this solution, I was hoping someone could tell me if this is correct or show me where I've gone wrong.
I'll let the bases for the subspace be [a,b,c]T
(my T's mean transpose)
---
I have the defintion for vector projection
p = (<u,v>/<v,v>)*v
---
I know v will be the [a,b,c]T vector but what is u?
The only thing I could think of is let it be the triplet [x,y,z]T which could be any vector in R3.
---
Using this I get
p = [(a/(a^2 + b^2 + c^2))(ax + by + cz)]
[(b/(a^2 + b^2 + c^2))(ax + by + cz)]
[(c/(a^2 + b^2 + c^2))(ax + by + cz)]
---
I'm not very confident with this solution, I was hoping someone could tell me if this is correct or show me where I've gone wrong.