Lecture 14: Low Rank Changes in A and Its Inverse

Description

In this lecture, Professor Strang introduces the concept of low rank matrices. He demonstrates how using the Sherman-Morrison-Woodbury formula is useful to efficiently compute how small changes in a matrix affect its inverse.

Summary

If \(A\) is changed by a rank-one matrix, so is its inverse.
Woodbury-Morrison formula for those changes
New data in least squares will produce these changes.
Avoid recomputing over again with all data
Note: Formula in class is correct in the textbook.

Related section in textbook: III.1

Instructor: Prof. Gilbert Strang