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boyboy400
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Homework Statement
Prove that symmetric and antisymmetric matrices remain symmetric and antisymmetric, respectively, under any orthogonal coordinate transformation (orthogonal change of basis):
Directly using the definitions of symmetric and antisymmetric matrices and using the orthogonal transformation rules without reference to components.
Homework Equations
The Attempt at a Solution
Well If S is symmetric then Sij=Sji
and for any u and v in the R space we have u.Sv=Transpose(S)u.v=Su.v
and S under any change of basis would be S'=QSTranspose[Q]
but I don't know how to go further...I really appreciate if anyone can help me out with this...I just have a few hours left :(
Thank you so much