Lecture 30: Completing a Rank-One Matrix, Circulants!

Description

Professor Strang starts this lecture asking the question “Which matrices can be completed to have a rank of 1?” He then provides several examples. In the second part, he introduces convolution and cyclic convolution.

Summary

Which matrices can be completed to have rank = 1?
Perfect answer: No cycles in a certain graph
Cyclic permutation \(P\) and circulant matrices
\(c_0 I + c_1 P + c_2 P^2 + \cdots\)
Start of Fourier analysis for vectors

Related section in textbook: IV.8 and IV.2

Instructor: Prof. Gilbert Strang