Consider the vector space http://www.physicsforums.com/latex_i.../1939559-0.pngnxn over http://www.physicsforums.com/latex_i.../1939559-1.png, let S denote the subspace of symmetric matrices, and R denote the subspace of skew-symmetric matrices. For matrices X,Yhttp://www.physicsforums.com/latex_i.../1939559-2.pnghttp://www.physicsforums.com/latex_i.../1939559-3.pngnxn define their inner product by <X,Y>=Tr(XTY). Show that, with respect to this inner product,

R=Shttp://www.physicsforums.com/latex_i.../1939559-4.png