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Symmetric matrices and orthogonal projections

  1. Apr 15, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider a symmetric n x n matrix A with A² = A. Is the linear transformation T(x) = Ax necessarily the orthogonal projection onto a subspace IR^n?


    2. Relevant equations



    3. The attempt at a solution
    No idea what thought to begin with.
     
  2. jcsd
  3. Apr 15, 2007 #2

    Dick

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    If A is symmetric over the reals then it can be diagonalized. What does that tell you? What is a projection?
     
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