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→案例
让我们来看一个<math>4 \times 5</math>矩阵的例子：
让我们来看一个<math>4 \times 5</math>矩阵的例子：
<math>
<math>
\mathbf{U} = \begin{bmatrix}
\mathbf{U} = \begin{bmatrix}
\color {Green}0&\color {Blue}-1&\color {Cyan}0&\color {Emerald}0 \\
\color {Green}0&\color {Blue}-1&\color {Cyan}0&\color {Emerald}0 \\
-1 & 0 & 0 & 0 \\
color {Green}-1&\color {Blue}0&\color {Cyan}0&\color {Emerald}0 \\
0 & 0 & 0 & -1 \\
color {Green}0&\color {Blue}0&\color {Cyan}0&\color {Emerald}-1 \\
0 & 0 & -1 & 0
color {Green}0&\color {Blue}0&\color {Cyan}-1&\color {Emerald}0
\end{bmatrix}
\end{bmatrix}
</math>
</math>
<math>
<math>
\mathbf{\Sigma} = \begin{bmatrix}
\mathbf{\Sigma} = \begin{bmatrix}
3 & 0 & 0 & 0 & 0 \\
3&0&0&0&\color {Gray{\mathit {0}}} \\
0 & \sqrt{5} & 0 & 0 & 0 \\
0&{\sqrt {5}}&0&0&\color {Gray}{\mathit {0}} \\
0 & 0 & 2 & 0 & 0 \\
0&0&2&0&\color {Gray}{\mathit {0}} \\
0 & 0 & 0 & 0 & 0
0&0&0&\color {Red}\mathbf {0} &\color {Gray}{\mathit {0}}
\end{bmatrix}
\end{bmatrix}
</math>
</math>
<math>
<math>
\mathbf{V}^* = \begin{bmatrix}
\mathbf{V}^* = \begin{bmatrix}
0 & 0 & -1 & 0 & 0 \\
color {Violet}0&\color {Violet}0&\color {Violet}-1&\color {Violet}0&\color {Violet}0 \\
-\sqrt{0.2} & 0 & 0 & 0 & -\sqrt{0.8} \\
color {Plum}-{\sqrt {0.2}}&\color {Plum}0&\color {Plum}0&\color {Plum}0&\color {Plum}-{\sqrt {0.8}} \\
0 & -1 & 0 & 0 & 0 \\
color {Magenta}0&\color {Magenta}-1&\color {Magenta}0&\color {Magenta}0&\color {Magenta}0 \\
0 & 0 & 0 & 1 & 0 \\
color {Orchid}0&\color {Orchid}0&\color {Orchid}0&\color {Orchid}1&\color {Orchid}0 \\
-\sqrt{0.8} & 0 & 0 & 0 & \sqrt{0.2}
color {Purple}-{\sqrt {0.8}}&\color {Purple}0&\color {Purple}0&\color {Purple}0&\color {Purple}{\sqrt {0.2}}
\end{bmatrix}
\end{bmatrix}
</math>
</math>