##############################

# Define matrix as column (document) array

A <- matrix ( c(
    c (1, 1, 3, 4, 5),  # First document
    c (3, 2, 1, 4, 3),
    c (1, 1, 3, 1, 2),
    c (2, 2, 4, 3, 5),
    c (3, 4, 3, 2, 1),
    c (3, 2, 3, 4, 4)), # Sixth document
    nrow = 5, # terms
    ncol = 6); # documents

# Print matrix A
A;

# Plot two arbitrary coordinates
plot (A[1,],A[2,]);

######################################

# Compute the principal component analysis
PCA <- princomp (t(A));

# Print the relevant results of the PCA
PCA$center;
PCA$loadings;

# Change the coordinates based on the eigenvector decomposition
A1 <- (t(PCA$loadings[,1:2])) %*% (A - PCA$center);

# Print the new coordinates
A1;

# Plot the two first (principal) coordinates in the new reference frame
plot (A1[1,],A1[2,]);