Linear Algebra and Its Applications · Problem 10

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition

Problem

Suppose

A

is a 2 by 2 symmetric matrix with unit eigenvectors

u_1

and

u_2

. If its eigenvalues are

\lambda_1 = 3

and

\lambda_2 = -2

, what are

U

\Sigma

, and

V^T