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Easy decomposition question

  1. Apr 28, 2009 #1
    My book says that, given a 4x4 rank-3 matrix Q (also positive-definite) and its spectral decomposition (eg, eigen decomposition),

    [tex]
    Q = V D V^{-1}
    [/tex]

    it is easy to factor Q as

    [tex]
    Q = H J H ^\mathsf{T}
    [/tex]

    where

    [tex]
    J = \left[
    \begin{array}{cccc}
    1 & 0 & 0 & 0\\
    0 & 1 & 0 & 0\\
    0 & 0 & 1 & 0 \\
    0 & 0 & 0 & 0
    \end{array}
    \right]
    [/tex]


    Apparently it's so trivial that they didn't waste the space to say how, but I'm not seeing how to do it...
     
  2. jcsd
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