Lecture 17: Rapidly Decreasing Singular Values

Description

Professor Alex Townsend gives this guest lecture answering the question “Why are there so many low rank matrices that appear in computational math?” Working effectively with low rank matrices is critical in image compression applications.

Summary

Professor Alex Townsend's lecture
Why do so many matrices have low effective rank?
Sylvester test for rapid decay of singular values
Image compression: Rank \(k\) needs only \(2kn\) numbers.
Flags give many examples / diagonal lines give high rank.

Related section in textbook: III.3

Instructor: Prof. Alex Townsend