Nog OP, but i think they are referring to the fact that you can use PCA (principal component analysis) on a matrix of datapoints to approximate it. Works out of the box in scikit-learn.

You can do (lossy) compression on rows of vectors (treated like a matrix) by taking the top N eigenvectors (largest N eigenvalues) and using them to approximate the original matrix with increasing accuracy (as N grows) by some simple linear operations. If the numbers are highly correlated, you can get a huge amount of compression with minor loss this way.

Personally I like to use it to visualize linear separability of a high dimensioned set of vectors by taking a 2-component PCA and plotting them as x/y values.