
110 Transformations
This is the primal problem for P C A (see the discussion of primal and dual
formulations for ridge regressio n in Section 2.6.4). Solution of the primal
problem can be performed directly from the ENVI main menu:
Transform/Principal Components/Forward PC Rotation
The Python and IDL programs in L istings 1.7 throug h 1.10 in Chapter 1
illustrated the procedure ex plic itly.
3.3.3 Dual solution
The normalized eigenvectors of the es tima ted cova riance matrix s a
re w
i
, i =
1 . . . N . These, as explained, are the principal vectors, and we now show how
to express them in terms of the e igenvectors of the Gram matrix GG
⊤
, which
was initia ...