# Generalized Wedderburn Rank Reduction

Source: [Generalized Wedderburn Rank Reduction](<https://www.sota2.com/research/paper/68fa5be81e209131ce9cc8cf>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:20:26.166Z

Authors: Oskar K\\k{e}dzierski

Published: 2024-06-06T12:07:38.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2406.03992>)

[PDF](<https://arxiv.org/pdf/2406.03992.pdf>)