In Gd, we verify that the diagonal elements have increased. Note the large off-diagonal elements. More importantly, there is no clear cut between high important factor combinations and unimportants ones. There is a smooth and unclear transition between significant and non-significant core elements.
In Gv, we can identify 5 clearly significant elements. And the gap between significant and non-significant core elements is between 18.75 and 5.39. The optimization of variance-of-squares re-enforces the significant elements found in the initial core, yielding a core that is easier to interpret.
With regards to verifying the orthogonality of the rotated and unrotated components matrices, it may be advisable to calculate the correlation matrices which should equal identity matrices in case of orthogonality. For the unrotated component matrices, and the transformation matrices from the core with optimal variance-of-squares, we may write this in MATLAB as:
>Ad=A*Od1;Bd=B*Od2;Cd=C*Od3; %Rotate the factors with optimal diagonality rotations
>Ad'*Ad, Bd'*Bd, Cd'*Cd %Verify the original component matrices
>Av=A*Ov1;Bv=B*Ov2;Cv=C*Ov3; %Rotate the factors with optimal var-of-sq. rotations
>Av'*Av, Bv'*Bv, Cv'*Cv %Verify the rotated component matrices