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Homework Help: Proving partitioned matrix involving conditional inverse

  1. Jul 27, 2010 #1
    1. The problem statement, all variables and given/known data

    For matrix X partitioned as [tex]\underline{X}[/tex] = [ [tex]\underline{X}[/tex]1 [tex]\underline{X}[/tex]2 ] with [tex]\underline{X}[/tex]1 matrix full column rank rx,

    2. Relevant equations
    prove that [tex]\underline{X}[/tex]([tex]\underline{X}[/tex]'[tex]\underline{X}[/tex])[tex]^{C}[/tex][tex]\underline{X}[/tex] = [tex]\underline{X'}[/tex][tex]_{1}[/tex]'([tex]\underline{X'}[/tex][tex]_{1}[/tex][tex]\underline{X}[/tex][tex]_{1}[/tex])[tex]^{-1}[/tex][tex]\underline{X'}[/tex][tex]_{1}[/tex]

    3. The attempt at a solution
    I would like to, but I don't have an idea how to solve this problem. I hope somebody can help me here.
    Last edited: Jul 28, 2010
  2. jcsd
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