Checking the orthogonality of P (loadings) matrix

One of the values we got in the script of the post:"Tutorials with Resemble (Part 3 - orthoProjection) " was the loadings matrix (X.loadings), or what we called usually in this blog the P matrix.

One of the characteristics of the loadings “P” matrix, when we develop the PCA, is that if we multiply it by its transpose we get the Identity Matrix “I”

P<-X.loadings

Pt<-t(X.loadings)

 

P%*%Pt = I

 

In the “I” matrix, its diagonal is “1”, and “0” values for all the rest cells indicating that all the loadings are orthogonal between them.

Exercise:

• Check it by yourself and take out the diagonal from the P matrix.
• Represent in a graphic the first loadings:
• 1 vs 2      : a plane
• 1, 2 and 3: a cube