In this post, I’m going to go over some examples of rank-one updates of matrices. To compute rank-one updates, we rely on the Sherman-Morrison-Woodbury theorem. From the previous post on Blockwise Matrix Inversion, recall that, given a matrix and its inverse
I’m taking a Statistics course on the theory of linear models, which covers Gauss-Markov models and various extensions of them. Sometimes, when dealing with partitioned matrices, and commonly Multivariate Normal Distributions, we’ll often need to invert matrices in a blockwise manner. This has happened often enough during this course (coincidentally was necessary knowledge for a midterm question), so I figured I should just document some of the inversion lemmas.