Yes! Same goes for pulling eigenvectors out of a data set e.g. for PCA (Principal Components Analysis) -- those form an orthonormal basis. You can even pick a s

Yes! Same goes for pulling eigenvectors out of a data set e.g. for PCA (Principal Components Analysis) -- those form an orthonormal basis. You can even pick a set of random orthogonal vectors of the same number and dimension as your original data and re-represent the data with no loss of information. I had a lot of fun demonstrating this concept for reconstructing images via a Processing sketch a few years ago and still use it for teaching from time to time. All source code for quick and dirty Haar, Eigen, Random, and Fourier-like methods included here: http://www.cc.gatech.edu/~phlosoft/transforms/ http://www.cc.gatech.edu/~phlosoft/transforms/