@article{drineas_ipsen_2019, title={LOW-RANK MATRIX APPROXIMATIONS DO NOT NEED A SINGULAR VALUE GAP}, volume={40}, ISSN={["1095-7162"]}, url={https://doi.org/10.1137/18M1163658}, DOI={10.1137/18M1163658}, abstractNote={This is a systematic investigation into the sensitivity of low-rank approximations of real matrices. We show that the low-rank approximation errors, in the two-norm, Frobenius norm and more generally, any Schatten p-norm, are insensitive to additive rank-preserving perturbations in the projector basis; and to matrix perturbations that are additive or change the number of columns (including multiplicative perturbations). Thus, low-rank matrix approximations are always well-posed and do not require a singular value gap. In the presence of a singular value gap, connections are established between low-rank approximations and subspace angles.}, number={1}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Drineas, Petros and Ipsen, Ilse C. F.}, year={2019}, pages={299–319} }