Projection Matrix Homework: Equations & Solution

AI Thread Summary
The discussion revolves around understanding projection matrices and their properties, specifically how to derive them from given vectors. Participants clarify that the projection matrix can be easily calculated by using the unit vector of the original vector, leading to a simplified matrix solution. There is also a query about how to format matrices in text, with suggestions to use LaTeX for proper representation. The conversation emphasizes the importance of filling out relevant equations to grasp the concepts fully. Overall, the thread highlights both the mathematical process and the formatting tools available for presenting solutions.
UOAMCBURGER
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Homework Statement


40756682_1595386137274940_7144466539691900928_n.png
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Homework Equations

The Attempt at a Solution


The solution is obviously given, but I don't really understand what is done there. What method is being used? so I can understand, because i see how they attained v, but then that vector normalised is not correct is it?
 

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You (and we) need the Relevant Equations filled out.

What is a Projection Matrix? What kinds of properties does it have that we can take for granted?
 
StoneTemplePython said:
You (and we) need the Relevant Equations filled out.

What is a Projection Matrix? What kinds of properties does it have that we can take for granted?
Don't worry, I learned how to solve it now. since you can find the projection matrix pretty easily then you just plug in the values from the given vector, here W (unit vector of v) the squares cancel the square roots and you're left with that matrix in solution P. But i was wondering how do you add a matrix into the text?
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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