Linear Algebra and Its Applications · Problem 6.3.5

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition

Problem

Compute

A^T A

and

AA^T

, and their eigenvalues and unit eigenvectors, for

A = \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}.

Multiply the three matrices

U\Sigma V^T

to recover

A