- #1
ahamdiheme
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Homework Statement
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,
R=S[tex]\bot[/tex]
Homework Equations
Definition of inner product
Definition of orthogonal compliment
Definition of symmetric matrix
Definition of skew symmetric matrix
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?