If c is a skew-symmetric matrix of order n and x is n 1 column matrix, then xt cx is a
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The term X′AX is also∑k,lxkAk,lxl
which is, when reversing the variables of summation,∑k,lxlAl,kxk=X′A′X
your mistake is that (CD)T is DTCT, not CTDT.
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