PCA & PCA: Get angle between pc1-pc2 planes

A command to calculate the angle between two planes. Each plane is spanned by the first two eigenvectors from the corresponding PCA.

## Algorithm

The algorithm is described in section 12.4.3 of Golub & van Loan (1996):

First we form the projection of one set of eigenvectors on the other set. This results in a 2×2 matrix C:

C = E1′ E2,

where E1 and E2 are 2×dimension and dimension×2 matrices that contain the first two eigenvectors of the PCA's, respectively.

Next, we compute the singular value decomposition of C:

C = U D V′

Now the cosine of the angle between the two planes is given by the second singular value σ2 and the angle in degrees is therefore:

arccos (σ2)·180/π