Using rank-one updates to fold new observations into the DMD linear operator without recomputing a full matrix inverse.
An introduction to dynamic mode decomposition, which splits spatiotemporal data into spatial modes and their time dynamics. I derive the algorithm using a truncated SVD, with resting-state MRI as the motivating use case.
Using the Sherman-Morrison-Woodbury identity to update a matrix inverse after a low-rank change. The example is updating linear regression coefficients with a new observation without refitting the model.
Deriving each block of the inverse of a 2x2 partitioned matrix using the Schur complements of A and D. I kept running into these identities in a linear models course, including on a midterm.