Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD): 행렬을 분해하는 방법 (Square, Symmetric 상관없이)

 

$\boldsymbol{A}=\boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T$

 

$\boldsymbol{A}\in \mathbb{R}^{m\times n}$

$\boldsymbol{U}\in \mathbb{R}^{m\times m}$ orthogonal matrix

$\boldsymbol{\Sigma}\in \mathbb{R}^{m\times n}$ diagonal matrix

$\boldsymbol{V}\in \mathbb{R}^{n\times n}$ orthogonal matrix

 

$\boldsymbol{V}$에서 orthogonal 하던 vector 가 $\boldsymbol{U}$에서도 orthogonal 한지를 보기 위함