MIT
Lecture 30: Completing a Rank-One Matrix, Circulants!
Science & MathMathematicsEngineeringElectrical Engineering
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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