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Show that PL has matrix

  1. Mar 27, 2008 #1
    Let PL an QL denote, respectively, projection on and reflection in the line L through the origin with direction vector d = [a b c] =not 0

    I got a proplem showing that PL is a matrix.

    1/(a^2 +b^2+c^) = Matrix......a^2 ab ac
    ..........................................ab b^2 bc
    ..........................................ac bc c^2
     
  2. jcsd
  3. Mar 27, 2008 #2

    HallsofIvy

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    Strictly speaking, PL is a linear transformation. You are talking about it's matrix representation in the basis in which the given line has direction vector with components [a b c]. Now, unfortunately, I have no idea what you mean by "1/(a^2+ b^2+ c^2)= Matrix ...!

    Given a vector [x y z], how would you find its projection, PL[x y z]? I get that the matrix representation is a very simple diagonal matrix.
     
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