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Homework Help: Orthogonal Complement

  1. Nov 2, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the vector space [tex]\Re[/tex]nxn over [tex]\Re[/tex], let S denote the subspace of symmetric matrices, and R denote the subspace of skew-symmetric matrices. For matrices X,Y[tex]\in[/tex][tex]\Re[/tex]nxn define their inner product by <X,Y>=Tr(XTY). Show that, with respect to this inner product,

    2. Relevant equations

    Definition of inner product
    Definition of orthogonal compliment
    Definition of symmetric matrix
    Definition of skew symmetric matrix

    3. The attempt at a solution
    If i can show that
    will it be sufficient and how do i go about it?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 2, 2008 #2


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    Science Advisor

    What do you mean by [itex]R- S^{\bot}= 0[/itex]? To show that [itex]R= S^{\bot}[/itex] you must show that the inner product of any member of R with any member of S is 0, that's all.
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