(adsbygoogle = window.adsbygoogle || []).push({}); 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(X^{T}Y). Show that, with respect to this inner product,

R=S^{[tex]\bot[/tex]}

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

R-S^{[tex]\bot[/tex]}=0

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

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# Homework Help: Orthogonal Complement

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