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Projection question with eigenvalues and eigenvectors

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Let v be a non-zero (column) vector in Rn.

    (a) Find an explicit formula for the matrix Pv corresponding to the projection of Rn to the orthogonal complement of the one-dimensional subspace spanned by v.

    (b) What are the eigenvalues and eigenvectors of Pv? Compute the dimensions of the associated eigenspaces. Justify your answers


    3. The attempt at a solution

    Wouldn't the formula for the matrix Pv be the null space for v such that it has eigenvalues 0,1 or -1?
     
  2. jcsd
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