Linear Algebra and Its Applications · Problem 6.3.1

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition

Problem

Compute

A^T A

and its eigenvalues

\sigma_1^2

0

and unit eigenvectors

v_1

v_2

A = \begin{bmatrix} 1 & 4 \\ 2 & 8 \end{bmatrix}.