0.2. Symbols

To maintain consistency across the site, I used the following notations.

Common Symbols §

Symbols	Represents
$\mathbf{D}$	Diagonal matrix
$d_i$	Diagonal elements of a matrix
${\mathbf{e}}_i$	Elementary basis vectors

SVD Specific Symbols §

Symbols	Represents
$\mathbf{U}$	Left unitary matrix
$\mathbf{V}$	Right unitary matrix
$\mathbf{\Sigma }$	Diagonal like matrix with singular values
${\sigma }_i$	Singular values
${\mathbf{u}}_i$	Left unitary vectors
${\mathbf{v}}_i$	Right unitary vectors
$\hat{\mathbf{U}}$	Left unitary matrix for reduced SVD
$\hat{\mathbf{V}}$	Right unitary matrix for reduced SVD
$\hat{\mathbf{\Sigma }}$	Diagonal matrix with singular values for reduced SVD