- SVD：
$$
\forall \boldsymbol{A} \in \mathbb{R}^{m\times n},\ \boldsymbol{A} = \boldsymbol{U}\boldsymbol{\Sigma} \boldsymbol{V}^{T} \iff \forall i,\ \boldsymbol{A}\boldsymbol{v}_{i} = \sigma_{i}\boldsymbol{u}_{i}
$$
where ^0e39bf
-
- left singular matrices $\boldsymbol{U}\in \mathbb{R}^{m\times m}$ is orthonormal
- right singular matrices $\boldsymbol{V}\in \mathbb{R}^{n\times n}$ is orthonormal
- ==Where is this line?==
- ==Where is this line?== $\boldsymbol{U}$ is eigenvector matrix of $\boldsymbol{A}\boldsymbol{A}^\top$
- ==Where is this line?== $\boldsymbol{V}$ is eigenvector matrix of $\boldsymbol{A}^\top \boldsymbol{A}$
![[test#^0e39bf]]
The “==Where is this line?==” is not shown in the reference.
