M=H'H 일때 M은 nonnegative eigenvalue를 가짐을 증명

\[ M=H'H \]

\[ Mv = \lambda v\]

\[ v'Mv = \lambda v'v \]

\[ v'H'Hv = \lambda v'v \]

\[ (Hv)'Hv = \lambda v'v \]

\[ w = Hv, w'w \geq 0\]

\[ \lambda v'v \geq 0\]

\[ \lambda \geq 0\]

Proof done by ChatGPT.