Linear Algebra and Its Applications · Problem 6.3.9

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition

Problem

Explain how

U\Sigma V^T

expresses

A

as a sum of

r

rank-1 matrices in equation (3):

A = \sigma_1 u_1 v_1^T + \cdots + \sigma_r u_r v_r^T.