Generalized Wedderburn Rank Reduction
<|reference_start|>Generalized Wedderburn Rank Reduction: We generalize the Wedderburn rank reduction formula by replacing the inverse with the Moore--Penrose pseudoinverse. In particular, this allows one to remove the non--singularity of a certain matrix from assumptions. The results implies in a straightforward way Nystroem, CUR decompositions, meta-factorization, and a result of Ameli, Shadden. We investigate which properties of the matrix are inherited by the generalized Wedderburn reduction. Reductions leading to the best low-rank approximation are explicitly described in terms of singular vectors. We give a self--contained calculation of the range and the nullspace of the projection $A(BA)^+B$ and prove that any projection can be expressed in this way.<|reference_end|>
@article{kędzierski2024generalized,
    title={Generalized Wedderburn Rank Reduction},
    author={Oskar Kk{e}dzierski},
    journal={arXiv preprint arXiv:2406.03992},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03992},
    primaryClass={math.NA cs.NA}
}