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mikee
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Solving Proju(Proju(v))=Proju(v) Mathematically
- Thread starter mikee
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- Projection Proof
In summary, to solve the equation Proju(Proju(v))=Proju(v), you can use the equations for projections and check if the right side equals the left side. This can be done mathematically, although it may be more obvious when done geometrically. It is important to clarify which definition of projection is being used. Once this is established, the equation can be solved using the appropriate equations for projections.
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tiny-tim
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Hi mikee! 
It should be obvious from the definition …
what definition of projection are you using?
It should be obvious from the definition …
what definition of projection are you using?
- #3
mikee
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haha ok i think I've got it i can just use the equations for the projections and if the right side equals the left side viola ha thanks
Related to Solving Proju(Proju(v))=Proju(v) Mathematically
1. How do you solve Proju(Proju(v))=Proju(v) mathematically?
To solve this equation, you first need to understand what Proju(v) represents. Proju(v) is a projection operator that projects a vector v onto a subspace. Therefore, solving Proju(Proju(v))=Proju(v) means finding the vector v that, when projected onto a subspace and then projected again onto the same subspace, results in the same vector v.
2. What is the purpose of solving Proju(Proju(v))=Proju(v) mathematically?
The purpose of solving this equation is to find the vector v that is in the subspace being projected onto. This can be useful in various mathematical and scientific applications, such as in linear algebra and signal processing.
3. What are the steps to solve Proju(Proju(v))=Proju(v) mathematically?
The steps to solve this equation involve setting up the projection operator equations, substituting the definition of Proju(v) into the equation, simplifying, and solving for the vector v. The specific steps may vary depending on the context and the given information.
4. Are there any special cases to consider when solving Proju(Proju(v))=Proju(v) mathematically?
Yes, there are a few special cases to consider. If the subspace onto which the vector v is being projected is the same as the original vector v, then v will be the solution to the equation. Another special case is when the subspace is a null space, in which case the solution will be the zero vector.
5. Can you provide an example of solving Proju(Proju(v))=Proju(v) mathematically?
Yes, let's say we have a vector v=[2, 4, 6] and we want to project it onto the subspace spanned by the vectors [1, 0, 0] and [0, 1, 0]. Using the projection operator formula, we can set up the equations as follows: Proju(v)=[2, 4, 0] and Proju(Proju(v))=[2, 4, 0]. We can then substitute these into the original equation and solve for v, which will result in v=[2, 4, 0] as the solution. This means that the vector v is already in the subspace being projected onto.
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