• As we mentioned earlier, PCA can be regarded as a specific case of SVD. Here, we generate the orthogonal vector from the swiss data from SVD and obtain the rotation from prcomp. We can see that the two generated matrices are the same:

        > svd.m = svd(scale(swiss))
        > svd.m$v
        Output
                    [,1]        [,2]         [,3]       [,4]        [,5]
        [1,]  0.52396452 -0.25834215  0.003003672 -0.8090741  0.06411415
        [2,] -0.57185792 -0.01145981 -0.039840522 -0.4224580 -0.70198942
        [3,] -0.49150243  0.19028476  0.539337412 -0.3321615  0.56656945
        [4,]  0.38530580  0.36956307  0.725888143  0.1007965 -0.42176895
        [5,]  0.09167606  0.87197641 -0.424976789 -0.2154928  0.06488642
        > pca.m = prcomp(swiss,scale=TRUE)
       > pca.m$rotation
         Output
                             PC1         PC2          PC3        PC4  
         PC5
        Agriculture      0.52396452 -0.25834215  0.003003672 -0.8090741
        0.06411415
        Examination  -0.57185792 -0.01145981 -0.039840522 -0.4224580 
        -0.70198942
        Education       -0.49150243  0.19028476  0.539337412 -0.3321615  
        0.56656945
        Catholic          0.38530580  0.36956307  0.725888143  0.1007965
        -0.42176895
        Infant.Mortality 0.09167606 0.87197641 -0.424976789 -0.2154928
        0.06488642