Lecture 34: Distance Matrices, Procrustes Problem

Description

This lecture continues the review of distance matrices. Professor Strang then introduces the Procrustes problem, which looks for the orthogonal matrix that swings one set of vectors as nearly as possible onto a second set.

Summary

Distance problem: Find positions \(x\) from distances between them.
Necessary and sufficient: Distances satisfy triangle inequality.
Procrustes: Given \(n\) vectors \(x\) and \(n\) vectors \(y\).
Find the orthogonal matrix \(Q\) so that \(Qx\)'s are closest to \(y\)'s.

Related sections in textbook: IV.9 and IV.10

Instructor: Prof. Gilbert Strang