Woodbury Matrix Identity

The Woodbury matrix identity, named after Max A. Woodbury, is a formula in linear algebra for computing the inverse of a matrix after it has been given a rank k correction, by instead performing a related rank k correction to the inverse of the original matrix. It is also known as the matrix inversion lemma or the Sherman-Morrison-Woodbury formula, and the identity appeared in earlier academic papers before Woodbury own report on it. The identity holds not only for ordinary matrices but more generally within rings and Ab-categories, and it allows an inverse or a solution to a linear system to be computed efficiently once a related inverse is already known, though its numerical stability is not fully understood and can be poor even for well conditioned matrices. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/