我怎样才能在 LaTeX 中实现这个公式？

Question

如何在LaTeX中实现图片中的公式？

Answer 1

这看起来就像你想要的：

\documentclass{article}
\usepackage{amsmath}

\renewcommand{\theequation}{4.\arabic{equation}}
\setcounter{equation}{5}

\begin{document}
    \begin{align}
        A + \delta \hat{A} &= \begin{bmatrix} \hat{Q}_t\\\hat{Q}_b\end{bmatrix} R,&& \|\delta \hat{A}\| = O (\epsilon \|A\|),\\
        \hat{Q}_t^T \hat{Q}_t + \hat{Q}_b^T \hat{Q}_b &= I_n + \Delta_1,&&\|\Delta_1\|=O(\epsilon),\\
        \hat{Q}_t^T \hat{Q}_t - \hat{Q}_b^T \hat{Q}_b &= \hat{L}^T \hat{L} + \Delta_2,&& \Delta_2^T = \Delta_2,~ \|\Delta_2\|_2 = O(\epsilon).
    \end{align}
\end{document}

Answer 2

像这样：

使用该mathtools包，定义新的分隔符对：

\documentclass{article}
\usepackage{amssymb, mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}

\renewcommand{\theequation}{4.\arabic{equation}}
\setcounter{equation}{5}

\begin{document}

    \begin{align}
A + \delta \hat{A} 
    & = \begin{bmatrix} \hat{Q}_t   \\  \hat{Q}_b\end{bmatrix} R,
        &&      \norm*{\delta \hat{A}} = O (\epsilon \norm*{A}),\\
\hat{Q}_t^T \hat{Q}_t + \hat{Q}_b^T \hat{Q}_b
    & = I_n + \Delta_1,
        &&  \norm*{\Delta_1}=O(\epsilon),\\
\hspace{-1.2cm}\hat{Q}_t^T \hat{Q}_t - \hat{Q}_b^T \hat{Q}_b
    & = \hat{L}^T \hat{L} + \Delta_2,
        &&  \Delta_2^T = \Delta_2, \norm*{\Delta_2}_2 = O(\epsilon).
    \end{align}

\end{document}