M=H'H 일때 M은 nonnegative eigenvalue를 가짐을 증명

$$M=H^{\prime }H$$

$$Mv=\lambda v$$

$$v^{\prime }Mv=\lambda v^{\prime }v$$

$$v^{\prime }{H}^{\prime }Hv=\lambda v^{\prime }v$$

$$(Hv{)}^{\prime }Hv=\lambda v^{\prime }v$$

$$w=Hv,w^{\prime }w\ge 0$$

$$\lambda v^{\prime }v\ge 0$$

$$\lambda \ge 0$$

Proof done by ChatGPT.