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How to prove that an orthogonal projection matrix is idempotent

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that [P]^2=[P] (that the matrix is idempotent)

    2. Relevant equations

    3. The attempt at a solution

    A(A^T*A)^-1 A^T= (A(A^T*A)^-1 A^T)^2

    Where A^T is the transpose of A. I have no idea.
  2. jcsd
  3. Apr 18, 2010 #2

    D H

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    Staff Emeritus
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    What is the relationship between your matrix A and your matrix P?

    Backing up a bit further, what is the definition of an orthogonal projection matrix?
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