Linear Algebra and Its Applications · Problem 17

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition-polar-decomposition

Problem

Diagonalize

A^TA

to find its positive definite square root

S = V\Sigma^{1/2}V^T

and its polar decomposition

A = QS

A = \frac{1}{\sqrt{10}} \begin{bmatrix} 10 & 6 \\ 0 & 8 \end{bmatrix}.