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We introduce a Generalized LU-Factorization (\textbf{GLU}) for low-rankmatrix approximation. We relate this to past approaches and extensively analyzeits approximation properties. The established deterministic guarantees arecombined with sketching ensembles satisfying Johnson-Lindenstrauss propertiesto present complete bounds. Particularly good performance is shown for thesub-sampled randomized Hadamard transform (SRHT) ensemble. Moreover, thefactorization is shown to unify and generalize many past algorithms. It alsohelps to explain the effect of sketching on the growth factor during GaussianElimination.

An improved analysis and unified perspective on deterministic and randomized low rank matrix approximations