We had three matrices from Jolliffe, P, V, and Q. They were allegedly a set of principal components P, a varimax rotation V of P, and a quartimin “oblique rotation” Q.

I’ll remind you that when they say “oblique rotation” they mean a general change-of-basis. A rotation preserves an orthonormal basis; a rotation cannot transform an orthonormal basis to a non-orthonormal basis, and that’s what they mean — a transformation from an orthonormal basis to a non-orthonormal basis, or possibly a transformation from a merely orthogonal basis to a non-orthogonal one. In either case, the transformation cannot be a rotation.

(It isn’t that complicated! If you change the lengths of basis vectors, it isn’t a rotation; if you change the angles between the basis vectors, it isn’t a rotation.)

Anyway, we showed in Part 1 that V and Q spanned the same 4D subspace of .

Now, what about V and P? Let me recall them:

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