The Arnoldi iteration is two things: the basis of many of the iterative algorithms of numerical linear algebra and, more specifically, a technique for finding eigenvalues of nonhermitian matrices.

Transforming a dataset into one with fewer columns is more complicated than it might seem, explains Dr. James McCaffrey of Microsoft Research in this full-code, step-by-step machine learning tutorial.

But computing eigenvalues and eigenvectors directly is extremely difficult. However, it's possible to compute eigenvalues and eigenvectors indirectly using singular value decomposition (SVD).