1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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')
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple matrix question?
  1. Simple matrix question (Replies: 1)

  2. Matrix question (Replies: 8)

  3. Simple matrix help (Replies: 5)

  4. Matrix question (Replies: 7)

Loading...