Video Lectures

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

Problems for Lecture 30
From textbook Section IV.8

3. For a connected graph with \(M\) edges and \(N\) nodes, what requirement on \(M\) and \(N\) comes from each of the words spanning tree?

From textbook Section IV.2

1. Find \(\boldsymbol{c\ast d}\) and \(\boldsymbol{c \circledast d}\) for \(\boldsymbol{c}=(2,1,3)\) and \(\boldsymbol{d}=(3,1,2)\).

Course Info

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As Taught In
Spring 2018
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Lecture Videos
Problem Sets
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