1.
Linear Algebra
C A (C^T) D A (C^T) C = C (A^T)
Tryed solving it for days, it's so hard, thank you very much to whoever manages to solve it,
please show your work too, thank you.
Solution
CA(C^(T))*DA(C^(T))*C=C(A^(T))
Multiply AC by AD to get A^(2)CD.
A^(2)CD(C^(T))(C^(T))*C=C(A^(T))
Multiply A^(2)CD by C to get A^(2)C^(2)D.
A^(2)C^(2)D(C^(T))(C^(T))=C(A^(T))
Multiply C^(T) by C^(T) to get C^(2T).
A^(2)C^(2)D(C^(2T))=C(A^(T))
Multiply A^(2)C^(2)D by each term inside the parentheses.
A^(2)C^(2T+2)D=C(A^(T))
Divide each term in the equation by A^(2)C^(2T+2).
(A^(2)C^(2T+2)D)/(A^(2)C^(2T+2))=(C(A^(T)))/(A^(2)C^(2T+2))
Simplify the left-hand side of the equation by canceling the common factors.
D=(C(A^(T)))/(A^(2)C^(2T+2))
Simplify the right-hand side of the equation by simplifying each term.
D=A^(T-2)C^(-2T-1)