Solving Proju(Proju(v))=Proju(v) Mathematically

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SUMMARY

The discussion centers on solving the equation Proju(Proju(v)) = Proju(v), where Proju(v) denotes the projection of vector v onto a subspace U. Participants emphasize the importance of understanding the definition of projection in a mathematical context. The solution involves applying the equations for projections to demonstrate that the left side equals the right side, confirming the identity. This mathematical approach clarifies the geometric intuition behind the projection operation.

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  • Understanding of vector projections in linear algebra
  • Familiarity with the concept of subspaces
  • Knowledge of mathematical equations related to projections
  • Basic skills in manipulating algebraic expressions
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Students studying linear algebra, mathematicians interested in vector spaces, and anyone looking to deepen their understanding of projection operations in mathematics.

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Homework Statement

How would i go about solving Proju(Proju(v))=Proju(v) Just a note Proju(v) means the projection of v onto you

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The Attempt at a Solution

how would i go about solving this is mathematical terms, it is obvious when you do it geometrically but I am just not sure how i would go about doing it mathematically
 
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Hi mikee! :smile:

It should be obvious from the definition …

what definition of projection are you using? :smile:
 
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
 

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