PCA -how are the principal components mapped?

Question

I have a problem with the pca in R, probably a simple one:

I have 10 Vectors a,b,c,d,e,f,g,h,i,j and bind them with cbind.

With the Result I perform a pca, using prcomp. I get the scores all right and also I get the principal components in descending order.

Only: how on earth do I know which of the components a to j is the first, which the second and so on?

Probably really a beginner's question - still cannot solve it and would appreciate some help.

Answer 1

The rotation matrix can tell you which original variables are important in each of the principal components. For example, the first column of the rotation matrix shows the contributions for PC1. A high value in the first row (relative to the other coefficients) means that the first original variable is important in the first principal component. Let's say that the first column has high positive values for the first five rows, and high negative values for the second five rows. This means that the PC axis can be interpreted as the ratio between those two groups.