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Simple matrix question?

  1. Sep 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove that if A is skew-symmetric (i.e. A = -A') then

    (I - A) . inv(I + A)

    is orthogonal, assuming that (I + A) is singular. inv(X) denotes inverse matrix of X. X' denotes transpose of X.

    3. The attempt at a solution

    I need to prove orthogonality :

    I know for square matrices : inv(XY) = inv(Y) . inv(X) and (XY)' = Y'X'

    So if X and Y were orthogonal then XY would be.

    But in this case X = I - A and Y = inv(I + A), but are they orthogonal?

    I also know that (I - A)' = (I + A)

    But cant figure it out. Do I have to resort to the defn of inv(X) = adj(X) / det(X) ?

    Would appreciate any clues... Thanks in advance
  2. jcsd
  3. Sep 19, 2011 #2
    Aha stupid me... I now note that inv(X)' = inv(X')
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