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将符号整齐地排列在一起

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将符号整齐地排列在一起

我试图将等号和大于号对齐，但似乎无法正确对齐（见附图）。我怎样才能正确对齐它们？我已在下面附上我的代码行。

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\begin{equation}
\begin{aligned}
E\big[\widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}\big] = E\Bigg[max\Bigg\{h_i(X_i^{j_1...j_i}),\frac{1}{b}\sum_{j=1}^{b} \widehat{V}_{i+1}^{j_1...j_ij}\Bigg\}|X_i^{j_1...j_i}\Bigg] \\

\geq max\Bigg\{h_i(X_i^{j_1...j_i}),E\Bigg[\frac{1}{b}\sum_{j=1}^{b} \widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}\Bigg]\Bigg\} \\ 

= max\Big\{h_i(X_i^{j_1...j_i}),E\big[\widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}\big]\Big\} \\ 

\geq max\Big\{h_i(X_i^{j_1...j_i}),E\big[V_{i+1}\big(X_{i+1}^{j_1...j_i1}\big)|X_i^{j_1...j_i}\big]\Big\} \\ 

= V_i\big(X_i^{j_1...j_i}\big).
\end{aligned}
\end{equation}

答案1

除了&在五个地方提供对齐点之外，您还应该 (a)\max用 代替\max和 (b) 使用大|符号（写成\bigm\vert和\biggm\vert）。请将所有 替换为...。\dots我还建议您使用直立的 E 字母来表示期望运算符。请写\bigl(和\bigr)等，而不仅仅是\big(和\big)；这样，LaTeX 可以优化打开和关闭“栅栏”符号周围的间距。最后但并非最不重要的是，不要将栅栏符号写得太大；例如，不要写\Biggl[什么时候\biggl[也一样好——或者可以说，甚至更好！

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\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\E}{E}
\begin{document}

\begin{equation}
\begin{aligned}
\E\bigl[\,\widehat{V}_i^{j_1\dots j_i}\bigm\vert X_i^{j_1\dots j_i}\bigr] 
&= \E\biggl[\max\biggl\{h_i(X_i^{j_1\dots j_i}),\frac{1}{b}\sum_{j=1}^{b} 
   \widehat{V}_{i+1}^{j_1\dots j_ij}\biggr\} \biggm\vert X_i^{j_1\dots j_i}\biggr] \\
&\ge \max\biggl\{h_i(X_i^{j_1\dots j_i}),\E\biggl[\frac{1}{b}\sum_{j=1}^{b} 
   \widehat{V}_{i+1}^{j_1\dots j_ij}\biggm\vert X_i^{j_1\dots j_i}\biggr]\biggr\} \\ 
&= \max\bigl\{h_i(X_i^{j_1\dots j_i}),\E\bigl[\,\widehat{V}_{i+1}^{j_1\dots j_ij}
   \bigm\vert X_i^{j_1\dots j_i}\bigr]\bigr\} \\ 
&\ge \max\bigl\{h_i(X_i^{j_1\dots j_i}),
   \E\bigl[\,V_{i+1}\bigl(X_{i+1}^{j_1\dots j_i1}\bigr)
   \bigm\vert X_i^{j_1\dots j_i}\bigr] \bigr\} \\ 
&= V_i\bigl(X_i^{j_1\dots j_i}\bigr)\,.
\end{aligned}
\end{equation}
\end{document}

答案2

您忘记了 & 符号......max可能是运算符\max：

\documentclass{article}
\usepackage{mathtools}

\begin{document}
    \begin{equation}
\begin{aligned}
E\big[\widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}\big] 
    & = E\Bigg[\max\Bigg\{h_i(X_i^{j_1...j_i}),\frac{1}{b}\sum_{j=1}^{b}
            \widehat{V}_{i+1}^{j_1...j_ij}\Bigg\}|X_i^{j_1...j_i}\Bigg] \\
    & \geq \max\Bigg\{h_i(X_i^{j_1...j_i}),E\Bigg[\frac{1}{b}\sum_{j=1}^{b}
            \widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}\Bigg]\Bigg\} \\
    & = \max\Big\{h_i(X_i^{j_1...j_i}),E
            \big[\widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}\big]\Big\} \\
    & \geq \max\Big\{h_i(X_i^{j_1...j_i}),E
            \big[V_{i+1}\big(X_{i+1}^{j_1...j_i1}\big)|X_i^{j_1...j_i}\big]\Big\} \\
    & = V_i\big(X_i^{j_1...j_i}\big).
\end{aligned}
    \end{equation}
\end{document}

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答案3

另一个解决方案是使用\DeclarePairedDelimiter及其变体，来自mathtools：这允许我们声明\E和\Set命令，该命令可以采用 中选择的可选参数，\big, \Big, \bigg, \Bigg它隐式地在分隔符周围添加了一对\bigl ... \bigr、 等。或者，有一个星号版本，它添加了一对\left ... \right。此外，垂直线被转换为\given命令，该命令的大小会根据分隔符的大小进行调整。请注意，在前两行中，我使用了较小的分隔符，我认为这更方便。

\documentclass{article}
\usepackage[utf8]{inputenc}%
\usepackage{mathtools}

\providecommand\given{}

\DeclarePairedDelimiterXPP\E[1]{\mathrm E}[]{}{%
\renewcommand\given{\nonscript\:\delimsize\vert\nonscript\:\mathopen{}}
#1}
\DeclarePairedDelimiterX\Set[1]\{\}{%
\renewcommand\given{\nonscript\:\delimsize\vert\nonscript\:\mathopen{}}
#1}
\begin{document}

\begin{equation}
\begin{aligned}
\E[\big]{\widehat{V}_i^{j_1...j_i}\given X_i^{j_1...j_i}} & = \E[\bigg]{\max\Set[\bigg]{\{h_i(X_i^{j_1...j_i}),\frac{1}{b}\sum_{j=1}^{b} \widehat{V}_{i+1}^{j_1...j_ij}}\given X_i^{j_1...j_i}} \\
 & \geq \max\Set[\bigg]{h_i(X_i^{j_1...j_i}), \E[\bigg]{\frac{1}{b}\sum_{j=1}^{b} \widehat{V}_{i+1}^{j_1...j_ij}\given X_i^{j_1...j_i}}} \\
 & = \max\Set[\Big]{h_i(X_i^{j_1...j_i}),\E[\big]{\widehat{V}_{i+1}^{j_1...j_ij}\given X_i^{j_1...j_i}}} \\
 & \geq \max\Set[\Big]{h_i(X_i^{j_1...j_i}),\E[\big]{V_{i+1}\bigl(X_{i+1}^{j_1...j_i1}\bigr)\given X_i^{j_1...j_i}}} \\
 & = V_i\bigl(X_i^{j_1...j_i}\bigr).
\end{aligned}
\end{equation}

\end{document}

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