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I have a question about this derivation. What is an example value of the actual matrix $A'$ such that $A'X=0$, $A'A=I$, and $\frac{1}{n}\Sigma((A'Y_{i}-mean(A'Y))^{2}=\frac{1}{(n-1)}\Sigma((Y_{i}-mean(Y))^{2}$, where the last formula comes from the formula for the ML estimate variance of the transformed problem equaling the REML estimate for the variance of the untransformed problem.

Note that $A'$ in the equations above also equals $C$ from this derivation.

Also, does $A'$ equal $K$ from this answer?

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