Extracting features or gene from PCA after calculating PCA for downstream analysis
The help page explains that there is a component which:


  rotation
  the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). The function princomp returns this in the element loadings.


So using using the rotation one can use it to calculate the importance of each feature in the input:

C &lt;- chol(S &lt;- toeplitz(.9 ^ (0:31))) # Cov.matrix and its root
set.seed(17)
X &lt;- matrix(rnorm(32000), 1000, 32)
Z &lt;- X %*% C  ## ==&gt;  cov(Z) ~=  C'C = S
pZ &lt;- prcomp(Z)
genesImportance &lt;- Z %*% pZ$rotation
genesImportance2 &lt;- pZ$x
all.equal(genesImportance, genesImportance2)
## [1] "Mean relative difference: 0.03680457"


This new matrix has the loading for each gene for each component. So you can now select them according to how much do they participate in each component or whatever you want. Or you can use it to predict the position of samples you didn't set in the initial data.