A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
For a projection matrix P, how can I prove that N(P)=R(IP) and also R(P)=N(IP) ?
 2 years ago
For a projection matrix P, how can I prove that N(P)=R(IP) and also R(P)=N(IP) ?

This Question is Open

hewsmike
 2 years ago
Best ResponseYou've already chosen the best response.0For this type of problem it might be best to think in wide angle. We are thinking of matrices  and in given instances we are asked to create them ie. produce the entries to place in each row and column  but there is an 'operational' concept also. So one can think of the identity matrix as the one which does 'nothing', as when applied to some vector it returns the same vector. And that is true for any vector it operates on. However the identity also projects any vector onto itself! :) However by projection matrix we ( usually ) intend to project any given vector onto/along some specific direction of interest. You already know how to do that along some 'special' directions  the coordinate axes  simply by plucking out one of the vector's components as expressed in that coordinate system. Or if you like take the dot/inner product of the vector of interest with a specific unit vector for some coordinate axis. For a general projection operation ( or operator ) you apply said operation to a vector to 'resolve' or establish it in terms of two other vectors  the sum of which gives the original vector : dw:1359584340887:dw then from that operational definition it is clear that once you have resolved to some direction, then resolving that component yet again gives that component. Thus \[R = RP^{n}\]for any number of projection operations n. Specifically : \[R=RP\]thus\[RRP=0\]and \[R(IP)=0\]now because the normal vector is exactly that ( perpendicular ) then : \[NP = 0\]Now your second equation doesn't look right. Do you mean \[R(N)=P(IP)\]
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.