\[\begin{split}
\begin{aligned}
&\text{Let } A \in R^{200 \times 20},\text{rank}(A) = 20\\
&A = U\Sigma V^T\\
&\Longleftrightarrow
A =
\begin{bmatrix}
\boxed{\begin{matrix} \\ \\ \\ \\ \\ \, u_1 \, \\ \\ \\ \\ \\ \\ \end{matrix}} \!\!\!\!&
\boxed{\begin{matrix} \\ \\ \\ \\ \\ \, u_2 \, \\ \\ \\ \\ \\ \\ \end{matrix}} \!\!\!\!&
\boxed{\begin{matrix} \\ \\ \\ \\ \\ \, u_3 \, \\ \\ \\ \\ \\ \\ \end{matrix}} \!\!\!\!&
\cdots \!\!\!\!&
\boxed{\begin{matrix} \\ \\ \\ \\ \\ u_M \\ \\ \\ \\ \\ \\ \end{matrix}} \!\!\!\!&
\cdots \!\!\!\!&
\boxed{\begin{matrix} \\ \\ \\ \\ \\ u_{200} \\ \\ \\ \\ \\ \\ \end{matrix}}
\end{bmatrix}
\begin{bmatrix}
\boxed{\sigma_1 \phantom{\dfrac{}{}} \!\!} & 0 & 0 & \cdots & 0 \\
0 & \boxed{\sigma_2 \phantom{\dfrac{}{}} \!\!} & 0 & \cdots & 0 \\
0 & 0 & \boxed{\sigma_3 \phantom{\dfrac{}{}} \!\!} & \cdots & 0 \\
\vdots & \vdots & \vdots & \ddots \\
0 & 0 & 0 & \cdots & \boxed{\sigma_{20} \phantom{\dfrac{}{}} \!\!} \\
0 & 0 & 0 & \cdots & 0 \\
\vdots & \vdots & \vdots & & \vdots \\
0 & 0 & 0 & \cdots & 0 \\
\end{bmatrix}
\begin{bmatrix}
\boxed{\begin{matrix} & & & v_1^T & & & \end{matrix}} \\
\boxed{\begin{matrix} & & & v_2^T & & & \end{matrix}} \\
\vdots \\
\boxed{\begin{matrix} & & & v_{20}^T & & & \end{matrix}} \\
\end{bmatrix}
\tag{3.4.5}\\
&\Longleftrightarrow
A = \begin{bmatrix}\sigma_1u_1\ & \sigma_2u_2,\dots,\sigma_{20}u_{20}\end{bmatrix}
\begin{bmatrix}
\boxed{\begin{matrix} & & & v_1^T & & & \end{matrix}} \\
\boxed{\begin{matrix} & & & v_2^T & & & \end{matrix}} \\
\vdots \\
\boxed{\begin{matrix} & & & v_{20}^T & & & \end{matrix}} \\
\end{bmatrix}
\\
&\Longleftrightarrow A = \sigma_1u_1v_1^T + \sigma_2u_2v_2^T + \sigma_3u_3v_3^T + \dots
\end{aligned}
\end{split}\]