20 - Singular Value Decomposition

Polar Decomposition corollary

Let $\mathbb{F}=\mathbb{R}$ or $\mathbb{F}=\mathbb{C}$ then
Every matrix $A\in {\mathbb{F}}^{m\times n}$ with $m\ge n$ can be written as

$$A=U_{p}H$$

where

1. $U_p\in {\mathbb{F}}^{m\times n}$ has orthonormal columns
2. $H\in {\mathbb{F}}^{n\times n}$ is self-adjoint ($H^{\ast }=H$) and positive semi-definite