Projection Matrix Homework: Equations & Solution

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SUMMARY

The discussion focuses on the concept of Projection Matrices, specifically how to derive and utilize them in mathematical problems. The solution provided demonstrates the calculation of a Projection Matrix P using the formula P = ww^T, where W is a unit vector of v. The resulting matrix is P = (1/5) * [[4, -2], [-2, 1]]. Participants also discussed the use of LaTeX for formatting mathematical expressions in forum posts, recommending tools like Codecogs for equation editing.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly vectors and matrices.
  • Familiarity with the properties of Projection Matrices.
  • Basic knowledge of LaTeX for mathematical formatting.
  • Experience with mathematical problem-solving techniques.
NEXT STEPS
  • Research the properties and applications of Projection Matrices in linear transformations.
  • Learn how to derive Projection Matrices for different vector spaces.
  • Explore advanced LaTeX techniques for formatting complex mathematical equations.
  • Study the implications of using Projection Matrices in computer graphics and data science.
USEFUL FOR

This discussion is beneficial for students and professionals in mathematics, physics, computer science, and engineering who are working with linear algebra and need to understand Projection Matrices and their applications.

UOAMCBURGER
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Homework Statement


40756682_1595386137274940_7144466539691900928_n.png
[/B]

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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